UNIVERSITY  OF  CALIFORNIA 
LOS  ANGELES 


DYNAMOMETERS 


AND 


THE  MEASUREMENT  OF  POWER: 


A   TREATISE  ON  THE  CONSTRUCTION  AND 
APPLICATION  OF  DYNAMOMETERS; 


WITH  A  DESCRIPTION  OF  THE  METHODS  AND  APPARATUS  EMPLOYED 
IN  MEASURING  WATER-POWER. 


BY 

JOHN  J.  FLATHER,  Pn.B.,  M.M.E., 

PROFESSOR    OP    MECHANICAL     ENGINEERING,     PURDUE     UNIVERSITY; 
AUTHOR  OP  AMERICAN  EDITION  WILSON'S   "  STEAM-BOILERS." 


SECOND  THOUSAND. 
NEW    YORK: 

JOHN  WILEY  &  SONS, 

53  EAST  TENTH  STREET. 

1893. 


COPYRIGHT,  1892, 

BY 

J.  J.  FLATHER. 


ROBERT  DRUMMOND, 

Electrotyper, 

m  and  448  Pearl  St, 

New  York. 


FERRIS  BROS., 

Printers, 

326  Pearl  Street, 

New  York. 


TT 


*?$' 


PREFACE. 


THE  aim  in  the  following  pages  has  been  to  present 
in  convenient  form,  for  the  use  of  Technical  Students 
and  Engineers,  a  description  of  the  construction  and 
principles  of  action  of  the  various  types  of  Dynamom- 
eter employed  in  the  measurement  of  power. 

A  chronological  presentation  of  the  subject  has  not 
been  attempted,  as  many  of  the  forms  once  used  have 
entirely  disappeared  ;  with  very  few  exceptions  the 
various  types  discussed  are  those  now  in  use. 

In  the  measurement  of  the  mechanical  horse-power 
of  a  hydraulic  motor  the  effective  power  may  be  as- 
<4\  certained  by  means  of  a  friction-brake,  or  other  dyna- 
v^)  mometer,  under  any  given   conditions ;    but  as   these 
Y^may  be  such  that  the  maximum  power  of  the  wheel  is 
•  1  not  developed,  it  remains  for  the  Engineer  to  determine 
"    those  conditions  best  suited  to  the  wheel  under  con- 
sideration.     In  Chapter  VI  is  given  a  discussion  of  the 
methods  and  apparatus  in  use  for  ascertaining  the  effi- 
ciency of  a  given  wheel,  including  the  determination 
of  flow  in  rivers  and  streams. 

The  work  here  presented  has  been  used  as  the  basis 
of  a  course  of  lectures  to  Engineering  students,  and  is 


379424 


iv  PREFACE. 

the  outgrowth  of  a  series  of  articles  published  in  the 
A  merican  Machinist. 

In  its  preparation  free  use  has  been  made  of  numer, 
ous  publications  relating  to  the  subject,  and  references 
for  further  information  are  given  in  foot-notes  through- 
out the  text. 

Special  mention  is  due  Professor  Andrew  Jamieson,  of 
Glasgow,  for  use  of  matter  and  figures  from  his  "  Steam 
and  Steam-engines "  (London :  Chas.  Griffin  &  Co.;. 
The  writer  is  also  under  obligations  to  Professors  Jas. 
E.  Denton,  J.  Burkitt  Webb,  Dr.  Mansfield  Merriman, 
and  others. 

J.  J.  FLATHER. 

LAFAYETTE,  IND.,  August  i,  1892. 


CONTENTS. 


CHAPTER    I. 

PAGE 
tjf  TERMINATION   OF   DRIVING   POWER I 

Horse-power  from  number  of  men  employed — Friction  of 
shafting  in  mills  and  machine-shops — Horse-power  from 
width  of  belt. 

CHAPTER   II. 

FRICTION-BRAKES 19 

Prony  brakes— Proportions  of  small  brakes— Regulators- 
Water-cooled  brakes — Determination  of  brake-power — Belt 
brakes — Compensating  brakes  —  Rope  brakes — Rappard's 
band-brake — Brake  for  vertical  shafts — Materials  for  brake- 
blocks — Lubrication — Width  and  velocity  of  rubbing  surface. 

CHAPTER  III. 

ABSORPTION-DYNAMOMETERS 54 

Richards  dynamometer  —  Alden  dynamometer  —  Alden 
brake  used  to  test  locomotive — Froude  water-brake. 

CHAPTER    IV. 

TRANSMISSION-DYNAMOMETERS 72 

Morin  dynamometer  —  Webber  balance-dynamometer— 
Briggs  belt  dynamometer — Tatham  dynamometers — Other 
belt  dynamometers — Brackett  cradle-dynamometer — Webb 
floating  dynamometer  —  Hartig  dynamometer — Emerson 
power-scale — Van  Winkle  power-meter — Flather  hydraulic 
dynamometer — Indicator-cards  from  dynamometer. 


VI  CONTENTS. 

CHAPTER  V. 

PAGE 

POWER  REQUIRED  TO  DRIVE  LATHES 151 

Friction  in  lathes— Table  of  horse-power  for  small  lathes 
— Formula  for  horse-power  running  light — Weight  of  metal 
removed  per  hour  per  horse-power — General  deductions. 

CHAPTER    VI. 

MEASUREMENT  OF  WATER-POWER 165 

Efficiency  of  motors — Determination  of  weight  of  water — 
Tank-measurement  —  Current-meters  —  Float-measurements 
— Mid-depth  velocity  —  Water-meters  —  Weir-measurements 
— Coefficient  of  discharge — Hook-gauges — Flow  of  water  in 
pipes — Loss  of  head — Pressure-head. 


DYNAMOMETERS 

AND 

THE  MEASUREMENT  OF  POWER. 


CHAPTER   I. 

DETERMINATION   OF   DRIVING   POWER. 

IN  designing  a  modern  machine-shop  or  manufac- 
tory, and  in  estimating  the  cost  of  power  for  its 
working  plant,  an  accurate  knowledge  of  the  amount 
of  power  absorbed  by  the  different  machines  is  not 
only  desirable,  but  essential  to  economy  and  efficiency. 

If  the  power  required  is  not  known,  the  engine  or 
motor  provided  may  prove  incapable  of  driving  the 
work  ;  or,  on  the  other  hand,  the  motive  power  may 
be  largely  in  excess  of  that  required  :  in  either  case 
there  is  an  unnecessary  expense — in  the  first  case,  in 
remedying  the  evil,  and,  in  the  second,  in  the  daily  ex- 
penditure of  fuel  for  excess  of  power. 

So  also  in  fitting  up  a  factory:  if  a  more  accurate 
knowledge  of  the  power  required  to  drive  machine- 
tools  were  known,  there  would  be  a  greater  economy 
in  running  them.  The  writer  has  in  mind  a  case 


2  DYNAMOMETERS 

that  came  under  his  notice  a  few  years  ago,  in  which 
a  certain  wood-planer  had  its  countershaft  changed 
three  times— different  diameters  of  pulley,  and  differ- 
ent widths  of  belt,  and  finally  a  heavier  counter- 
shaft being  used — before  it  would  work  satisfactorily 
Machines  are  largely  belted  by  guesswork.  If  the. 
pulleys  guessed  at  are  nearly  large  enough  to  do  the 
work,  the  workman  stretches  his  belt  to  its  utmost, 
and  manages  to  run  the  machine  by  taking  light  cuts  ; 
if,  however,  the  belt  has  a  velocity  and  width  barely 
sufficient  to  run  the  machine,  and  an  ordinary  cut  will 
throw  off  the  belt,  then,  if  split  pulleys,  are  not  in  use, 
a  length  of  shafting  is  taken  down  and  a  larger  pulley 
put  in  the  place  of  the  one  which  has  shown  itself  to  be 
insufficient  to  drive.  Sometimes  both  a  greater  width 
of  belt  and  a  larger  pulley  have  to  be  resorted  to. 

Another  case  was  where  a  6-inch  belt  running  over 
a  36-inch  pulley  at  120  revolutions  per  minute  had 
been  put  in,  and  had  been  running  for  more  than  a 
year  driving  a  roomful  of  high-velocity  machines  used 
for  covering  magnet-wire.  Evenness  of  motion  is 
specially  desirable  in  this  class  of  machinery;  and  yet, 
when  all  the  machines  were  on,  the  shaft  would  vary 
from  80  revolutions  per  minute  to  its  normal  speed. 

Rosin  or  belt-oil  was  in  order  every  few  days,  and 
when  the  slip  became  too  great  the  engine  had  to  be 
shut  down  and  the  belt  relaced.  The  relacing  was 
done  by  the  use  of  clamps,  and  the  belt  finally  be- 
came so  taut  that  the  increased  friction  on  the  beat- 
ings near  the  driving-pulley  kept  the  boxes  and  shaft 
constantly  hot.  This  belt  was  a  continual  source  of 
annoyance  and  expense ;  but,  because  it  had  been 


AND    THE  MEASUREMENT  OF  POWER.  3 

deemed  large  enough  to  furnish  power  for  the  forty  or 
more  machines  in  the  room,  no  change  had  ever  been 
made,  and  it  had  run  for  over  a  year  in  this  same  manner. 

A  Q-inch  belt  was  put  on,  and  no  trouble  was 
afterwards  experienced,  though  it  has  now  been  run- 
ning  for  several  years.  It  is  easy  enough  to  remedy  a 
defect  like  this  ;  but  prevention  would  have  been 
better,  and  would  have  considerably  reduced  the 
expense  account.  The  knowledge  of  the  power  re- 
quired to  drive  the  machinery  was  wanting.  The 
question  arises  :  How  can  this  power  be  estimated  ? 

In  the  discussion  of  an  inquiry  as  to  the  power 
required  to  drive  machine-tools,  Mr.  G.  H.  Babcock 
stated  at  a  meeting  of  the  American  Society  of  Me- 
chanical Engineers*  that  for  a  general  rule  in  ordi- 
nary machine-work  we  may  take  roughly  one  horse- 
power as  sufficient  to  drive  machine-tools  necessary 
to  keep  ten  men  at  work  ;  but  this,  he  adds,  does  not 
necessarily  include  shafting,  engine,  etc.,  nor  blowers 
for  foundry  work. 

Expressed  algebraically,  this  rule  of  thumb  would 
be 


where  N  equals  the  number  of  men  employed  ;  or,  if 
we  let  10  =  C,  a  constant,  we  have 


-- 
H.P. 


*  Trans.  A.  S.  M.  E     vol.  vm. 


4  D  YNA  MOME  TERS 

The  above  as  it  stands  is  of  little  or  no  value  ;  in  the 
first  place,  C  is  too  large,  as  will  be  shown  by  the 
following  data,  obtained  from  a  large  nurrber  of  rep- 
re'sentative  machine-shops  ;  and,  in  the  second  place, 
the  power  required  to  drive  the  machinery  varies 
between  such  wide  limits,  even  in  the  same  class  of 
work,  that  separate  values  of  C  cannot  be  determined 
which  may  be  relied  upon  as  giving  even  a  rough  ap- 
proximation. 

Such  a  formula  is  of  value  only  when  C  has  been 
determined  for  two  or  more  similar  plants,  and  applied 
to  another  equipment  working  under  similar  condi- 
tions— and  this  indeed  is  rarely  met  with. 

By  a  reference  to  the  above  table  it  will  be  noticed 
that  two  firms  on  exactly  the  same  line  of  work — 
that  of  manufacturing  machine-screws — require  a  total 
horse-power  such  that  the  number  of  men  employed 
per  horse-power  is  in  the  one  case  2,  and  in  the  other 
0.62  ;  or  as  3  to  I.  The  small  value  of  C  in  both  cases 
is  evidently  due  to  the  nature  of  the  machinery,  which 
is  largely  automatic,  one  man  being  able  to  feed  several 
machines.  A  comparison  of  the  values  of  C  (obtained 
for  total  power  used)  of  two  well-known  firms,  the 
Pratt  &  Whitney  Manufacturing  Co.  and  the  Brown 
&  Sharpe  Manufacturing  Co.,  shows  that  the  latter 
employ  only  3.91  men  per  horse-power,  while  Pratt 
&  Whitney  employ  6.04  ;  and  yet  these  shops  may  be 
considered  to  belong  to  the  same  class. 

Another  comparison  of  two  firms  running  about 
the  same  class  of  machinery  is  that  of  the  Bald- 
win Locomotive  Works  and  William  Sellers  &  Co. 
The  Baldwin  Locomotive  Works  give  a  value  of 


AND   THE   MEASUREMENT  OF  POWER. 

!.,. 


d    H  I«>°X  -WJ    J 


3AUQ  O    "JJ  J3J 


3AUQ    oj    bay 


s|J 

Jt 


:     S 


u 


6  D  YNA  MOME  TEKS 

1.64  for  C  per  total  horse-power,  and  Sellers  &  Co. 
give  2.93.  If  we  deduct  the  power  required  to  run 
the  shafting  in  each  works,  the  values  become,  respec- 
tively, 

C,  —  8.20, 

C,  =  4-87. 

A  closer  result  obtains  between  the  Pond  Machine- 
Tool  Works  and  William  Sellers  &  Co.  throughout  all 
the  data  given.  The  percentage  of  power  required  to 
drive  shafting  is  in  one  case  41  per  cent.,  and  in  the 
other  40  per  cent.  The  values  of  C  and  C,  are  as  fol- 
lows : 

C.  Ci. 

Pond  Machine-Tool  Works 2.4  4.1 1 

William  Sellers  &  Co 2.93         4.87 


Average  ................    2.66         4.49 

These  values  are  sufficiently  close  to  enable  one  to 
deduce  an  approximate  value  for  C  and  Cl  which 
would  apply  to  either  case,  but  when  used  in  connec- 
tion with  other  and  similar  shops  the  results  could  not 
be  depended  upon,  even  roughly. 

Thus  the  average  value  of  C,  as  shown  above,  is 
2.66  per  total  horse-power.  Applied  to  Wm.  Sellers  & 
Co.  this  gives 


=  2.66  X  102.45, 

=  273  men  employed. 


AND  THE  MEASUREMENT  OF  POWER.  7 

Applied  to  Pond  Tool  Works : 

N=  2.66  x  1 80, 

=  478  men  employed. 

In  the  former  case  N  should  equal  300,  and  in  the 
latter  432.  These  results  are  only  rough  estimates, 
but  are  correct  to  within  10  per  cent  of  the  actual 
number  employed.  If  we  apply  the  formula  to  the 
Pratt  &  Whitney  Co.,  manufacturers  of  machine-tools, 
we  obtain  : 

N  =  2.66  X  120, 
=  319  men; 

whereas  we  find  from  the  table  that  725  are  employed. 

Looked  at  from  its  most  favorable  standpoint  by 
comparing  those  values  for  similar  grades  which  most 
nearly  agree,  it  will  be  seen  that  the  formula  is  really 
of  no  practical  value,  and  much  less  can  it  have  any 
weight  when  looked  at  from  an  engineering  stand- 
point. 

A  look  at  some  of  the  results  obtained  from  the 
data  given  may  prove  to  be  interesting. 

It  has  been  stated  that  ten  is  too  large  a  value  for 
the  number  of  men  employed  per  horse-power  when 
applied  to  machine-tools,  even  neglecting  the  power 
required  to  drive  the  shafting,  etc. 

The  average  value  of  C1  obtained  from  table  is  5.13, 
or  say  5.0 ;  while  the  minimum  value  is  0.833,  the 
maximum  being  10.25.  It  would  be  out  of  the  ques- 


8  D  YNA  MOME  TERS 

tion  to  apply  the  formula  with  the  average  value  of  £T,, 
viz.,  5.0,  to  either  of  these  cases  ;  nor  is  it  practicable 
to  apply  any  other  value  of  Cl  either  to  determine  the 
horse-power  from  the  number  of  men  employed,  or, 
vice  versa,  to  obtain  the  number  of  men  employed 
from  the  horse-power  furnished. 

It  will  be  noticed  in  the  sixth  column,  headed 
"  Per  cent  of  power  required  to  drive  shafting,"  that 
very  wide  differences  occur.  The  maximum  is  that 
used  by  the  Baldwin  Locomotive  Works,  viz.,  80  per 
cent — an  extremely  large  factor; — while  the  minimum 
given  by  J.  A.  Fay  &  Co.  is  only  15  per  cent;  the 
average,  38.6  per  cent,  corresponds  to  that  quoted  by 
William  Sellers  &  Co.  within  less  than  if  per  cent. 

Mr.  J.  T.  Henthorn,  in  a  paper  read  before  the 
American  Society  of  Mechanical  Engineers,  states  that 
the  friction  of  the  shafting  and  engine  in  a  print-mill 
should  not  exceed  19  per  cent  of  the  full  power.  Out 
of  fifty-five  examples  of  a  miscellaneous  character 
which  he  has  tabulated,  seven  cases  are  below  20  per 
cent,  twenty  vary  from  20  per  cent  to  25  per  cent,  fifteen 
from  25  per  cent  to  30  per  cent,  eleven  from  30  per  cent 
to  35  per  cent,  and  two  above  35  per  cent,  while  the 
average  of  the  total  number  is  25.9  per  cent. 

Mr.  Barrus,  speaking  of  this  subject,  quotes  eight 
cases,  the  data  of  which  were  obtained  from  tests  made 
by  himself  in  various  New  England  cotton-mills,  in 
which  the  minimum  percentage  was  18,  and  the  maxi- 
mum 25.7,  the  total  average  being  22  per  cent. 

Mr.  Samuel  Webber  states  that  16  per  cent  of  the 
total  power  of  a  mill  is  sufficient  to  overcome  the 
friction  of  shafting  and  engine — 10  per  cent  for  the 


AND  THE  MEASUREMENT  OF  POWER.  9 

shafting  alone.  But  in  this  estimate  Mr.  Webber 
does  not  include  the  loss  due  to  the  belts  running 
upon  loose  pulleys,  which  he  does  not  consider  to  be 
part  of  the  shafting,  as  they  are  not  so  running  while 
the  machinery  is  in  operation  :  and  when  it  is  not,  they 
may  be  thrown  off  as  well  as  not,  except  for  conven- 
ience. He  further  estimates,  both  from  his  own  ex- 
perience and  the  observations  of  others,  that  the  power 
consumed  by  the  machine-belts  on  the  loose  pulleys  in 
a  large  cotton-mill  is  about  8  per  cent  of  the  whole. 
This  8  per  cent  added  to  the  16  per  cent  loss  due  to 
shafting  and  engine  will  give  24  per  cent  of  the  total 
power — a  result  which  agrees  closely  with  the  average 
values  given  above. 

The  writer  believes  that  for  shops  using  heavy  ma- 
chinery the  percentage  of  power  required  to  drive  the 
shafting  will  average  from  40  to  50  per  cent  of  the 
total  power  expended.  This  presupposes  that  under 
the  head  of  shafting  are  included  elevators,  fans,  and 
blowers. 

In  shops  using  lighter  machinery  and  with  foundry 
connected  the  power  percentage  will  be  about  the 
same  as  above ;  but,  if  the  foundry  work  is  done  out- 
side, the  power  required  to  drive  the  shafting  will  not 
average  so  high,  the  range  being  about  10  per  cent  less, 
or  from  30  to  40  per  cent  of  the  total. 

In  machine-shops  with  a  line  of  main  shafting  run- 
ning down  the  centre  of  a  room,  connected  by  short 
belts  with  innumerable  countershafts  on  either  side, 
often  by  more  than  one  belt,  and,  as  frequently 
happens,  also  connected  to  one  or  more  auxiliary 


1 0  D  YNA  MO  ME  TEKS 

shafts  which  drive  other  countershafts,  we  can  see 
why  the  power  required  to  drive  this  shafting  in 
machine-shops  should  be  greater  than  that  found  in 
cotton  and  print  mills,  the  machinery  of  which  is  in 
general  driven  from  the  main  lines  of  shafting.  Nor 
can  we  neglect  the  loss  due  to  belts  upon  loose  pulleys, 
as  with  the  numerous  clutches  and  countershafts  in 
use  the  conditions  more  nearly  approach  those  which 
exist  when  the  machinery  is  in  operation.  There  is  no 
doubt,  however,  that  a  large  percentage  of  the  power 
now  spent  in  overcoming  the  friction  of  shafting  in  or- 
dinary practice  could  be  made  available  for  useful  work 
if  wider  and  looser  belts  were  employed,  or,  what  would 
have  the  same  effect,  if  the  belts  were  slackened  and 
their  speed  increased ;  and  also  if  more  attention  were 
paid  to  lubrication. 

As  the  power  required  to  drive  the  machinery  in  a 
modern  plant  cannot  be  even  approximately  ascer- 
tained from  its  relation  to  the  number  of  men  employed, 
the  question  still  remains  open :  How  can  this  power 
be  measured  ? 

One  method  frequently  used  is  that  by  which  the 
power  required  is  ascertained  from  the  velocity  and 
width  of  driving-belt.  Different  rules  have  been  given 
in  our  text-books  and  engineering  journals  in  order  to 
estimate  the  driving  power  of  a  belt  from  its  width  and 
velocity.  A  rule  which  the  writer  has  used  in  his  prac- 
tice when  the  difference  in  diameters  of  pulleys  is  not 
very  great  is  :  Every  inch  in  width  of  a  single  laced  belt, 
having  a  velocity  of  800  feet  per  minute,  will  transmit 
one  horse-power  up  to  a  velocity  of  about  5000  feet  per 
minute  ;  beyond  5000  the  centrifugal  force  of  the  belt 


AND  THE  MEASUREMENT  OF  POWER.  II 

largely  diminishes  its  power.     Expressed  as  a  formula 
we  have 


in  which  b  equals  breadth  of  belt  in  inches,  and  V  equals 
velocity  of  belt  in  feet  per  minute.  To  illustrate  this, 
let  us  look  at  an  example.  Suppose  the  main  shaft  of 
a  factory  runs  at  125  revolutions  per  minute,  and  a  12- 
inch  pulley  on  this  shaft  drives  a  lo-inch  pulley  on  the 
counter  of  a  i6-inch  lathe  through  a  3  inch  belt  ;  the 
lathe  is  driven  by  a  2^-inch  belt  running  from  a  lo-inch 
step  to  an  8-inch.  What  power  does  the  lathe  absorb 
when  the  belt  is  taxed  to  its  limit  ?  The  speed  of  the 
belt  is  392  feet  per  minute  ;  if  we  disregard  slip,  which 
is  about  two  per  cent  of  the  total  velocity,  this  would 
give 


Now,  as  shown,  the  belt  will  transmit  according  to 
our  formula  1.22  H.  P.,  and  by  calculating  H.  P.  for 
the  different  machines  in  the  factory  a  measure  of  the 
driving  power  may  be  obtained,  to  which  a  certain  per 
cent  should  be  added  for  power  required  to  drive  the 
shafting. 

This  process  might  give  an  approximation  somewhat 
nearer  the  truth  than  the  method  previously  discussed, 
but  as  the  formula  is  based  on  a  certain  permissible 
stress  in  the  belt-fibres,  which  stress  is  well  within  the 
limit  of  safety,  we  do  not  know  how  much  more  power 


1 2  D  YNAMOME  TERS 

the  belt  is  exerting,  nor  do  we  know  that  it  is  exerting 
as  much  as  the  formula  calls  for.  Although  we  can 
calculate  what  the  width  of  a  belt  ought  to  be  to  trans- 
mit a  given  horse-power,  x,  at  a  given  velocity,  the 
stress  in  the  belt  may  be  greater  or  less  than  that  on 
which  our  formula  is  based,  and  the  resulting  horse- 
power transmitted  may  be  x  ±  y. 

In  order  to  measure  the  amount  of  driving  power 
from  the  velocity  and  width  of  belting,  the  tension  on 
the  tight  and  slack  sides  of  a  belt,  the  arc  of  contact 
a  between  belt  and  pulley,  and  the  coefficient  of  fric- 
tion 0  are  all  necessary. 

The  width  of  a  belt  of  thickness  /  must  be  such  that 
its  cross-section  multiplied  by  its  permissible  working 
stress /is  capable  of  resisting  the  maximum  tension  7", 
in  the  driving  side  of  the  belt,  or  7",  =  btf. 

We  have  the  general  equation 


PV 

H.P.  =  ——> 
33000 


Now  if  we  let  P  =  — 1 .  where  m  is  a  function  of  the 
m 

arc  of  contact  a,  and  coefficient  of  friction  0,  we  obtain 

//./>  =      bffV 
33  ooo;« ' 

If  bt  =  one  square  inch,  the  horse-power  transmitted 
per  looo  feet  per  minute  is  expressed  by  //,  =  -^— . 


AND    THE  MEASUREMENT  OF  POWER.  13 

This  Reuleaux  calls  the  specific  duty  of  a  belt,  the 
value  of  which  he  gives  for  leather  belting,  as  varying 
from  5.3  to  9.8  ;  hence 


=  5-3  to  9.8. 


As  f  varies  in  different  belts,  and  ;//  varies  with  a 
and  0,  it  is  seen  that  any  general  formula,  whether 
rational  or  empirical,  is  not  trustworthy  when  the  total 
amount  of  power  absorbed  is  desired — however  satis- 
factory such  a  formula  may  be  when  used  to  calculate 
the  width  of  belt  to  transmit  safely  a  given  horse- 
power. The  only  reliable  method  of  determining  this 
transmission  of  power  is  by  the  use  of  some  form  of 
dynamometer. 

Where  power  is  rented  from  one  firm  to  another,  t4ie 
necessity  of  obtaining  correct  estimates  of  the  amount 
consumed  is  apparent.  A  case  in  point  is  that  of  the 
Lowell  Hosiery  Co.,  which  rented  an  estimated  total 
of  13^  horse-power,  for  which  $125  per  horse-power  per 
annum  was  paid. 

A  dynamometer  test  being  made,  it  was  ascertained 
that  28^  H.  P.  was  being  used — more  than  double  the 
amount  paid  for.  Another  case  is  that  of  the  North- 
ampton Tape  Co.,  whose  lease  called  for  30  H.  P.;  a 
dynamometer  being  applied  to  the  shaft  it  was  found 
that  ii  H.  P.  was  the  maximum  transmitted.  Still 
another  case  is  that  of  a  company  in  Worcester,  which 
hired  rooms  and  power,  the  basis  of  rent  being  esti- 
mated at  13  H.  P.  Forty  horse-power  was  actually 


1 4  D  YNA  MO  ME  TERS 

used,  as  shown  by  a  dynamometer  test,  and  the  rent 
was  increased  accordingly. 

Many  such  instances  could  be  cited  to  show  that  very 
wide  differences  exist  between  the  amount  of  estimated 
power  and  the  amount  actually  developed  as  deter- 
mined by  an  accurate  dynamometer.  Such  wild  es- 
timates are  at  first  sight  difficult  to  account  for,  since 
there  are  several  good  rules  in  use  for  ascertaining  the 
width  of  belt  to  transmit  a  given  horse-power;  however, 
as  already  shown,  as  these  rules  do  not  take  into 
count  the  individual  differences  in  belt-tension,  there 
will  result,  with  variations  of  velocity  and  tension,  cor- 
responding variations  of  power  transmitted. 

Mr.  Henry  R.  Towne's  experiments  with  leather 
belting  show  that  the  ultimate  strength  of  a  laced  belt 
^"  thick  is  about  200  pounds  per  inch  of  width ;  as- 
suming a  factor  of  safety  of  3,  this  gives  66  pounds  as 
the  allowable  strain  per  inch  of  width  in  single  belting 
(Morin  assumes  55  pounds).  For  a  spliced  or  riveted 
belt  the  permissible  strain  may  be  125  pounds  per  inch 
of  width. 

The  following  table,  compiled  by  Mr.  Nagle,  gives  a 
list  of  belts  in  use,  and  the  actual  horse-power  trans- 
mitted by  them,  compared  with  which  are  calculated 
widths  by  the  formulae  of  Webber  and  Nagle.  The 
widths  in  the  ninth  and  tenth  columns  have  been  calcu- 
lated by  the  writer  and  added  to  Mr.  Nagle's  table ; 
the  handy  rule  referred  to  in  the  last  column  being 
the  one  previously  mentioned,  namely, 


_  800  H.P. 
b-  _ 


AND    THE  MEASUREMENT  OF  POWER. 


TABLE    II. 
WIDTH  AND  VELOCITY  OF  BELTING. 


1 

^s 

A 

Width  of  Belt. 

if 

-S  « 

1 

c 

|.= 

v 

* 

.(- 

! 

jl 

ll 

fi 

jj. 

ic 

i 

JrtJ 

J 

II 

fl 

ll 

32 

Q 

s 

H 

e 

^ 

Z. 

o 

33 

375 

5,600 

60 

98 

Double 

24 

22 

34 

3*i 

27 

250 

3,080 

84 

58 

4-p'y 

48 

50 

28 

28 

23 

22O 

2,451 

42 

135 

Single 

22 

98 

31 

84 

70 

175 

3-179 

72 

93 

Double 

I9i 

25 

26 

22 

175 

3,629 

"Si 

55 

29 

15 

22 

23 

20 

130 

2,117 

70 

18 

18 

22 

29 

24i 

"5 

3,490 

84 

82 

Mi 

8 

17 

17 

go 

2,860 

60 

87 

12 

10 

15 

15 

"i 

77 

2,268 

60 

77 

Mi 

12 

12 

16 

I3i 

45 

2,000 

48 

37 

Si   gle 

20 

21 

15 

21 

18 

49 

2,111 

72 

24 

M 

21 

18 

21 

18^ 

43 

1,  800 

60 

44 

18 

20 

M 

23 

19 

41 

I.Sog 

60 

42 

1  74 

12 

16 

21 

18 

40 

2,OOO 

72 

37 

' 

8 

14 

13 

19 

16 

18 

850 

22 

116 

Double 

6 

19 

8 

IO 

8* 

8 

942 

30 

40 

Single 

7 

12 

8 

8 

7 

In  the  formula  used  by  Mr.  Nagle,  the  coefficient  of 
friction  deduced  from  the  experiments  of  Mr.  Towne 
is  assumed  at  42  per  cent.  As  this  coefficient  was 
obtained  while  the  belt  was  at  rest  or  had  no  apparent 
velocity,  the  friction  between  the  surface  of  the  pulley 
and  the  belt  will  be  somewhat  different  when  in  motion, 
although  the  experiments  made  by  Wm.  Sellers  &  Co., 
with  belting  running  at  an  average  velocity  of  800  feet 
per  minute,  give  coefficients  varying  from  25  per  cent 
to  100  per  cent.  Rankine  assumes  15  per  cent  as  the 
coefficient  of  friction,  but  the  results  of  all  other  inves- 
tigators show  this  value  to  be  too  low.  Morin  gives 


1 6  D  YNA  MO  ME  TERS 

28  per  cent  as  an  average  value  for  dry  belts  on  smooth 
cast-iron  pulleys,  and  12  per  cent  for  very  greasy  shop 
belts  on  cast-iron  pulleys — the  mean  of  these  being  20 
per  cent.  Recent  investigations  at  the  Massachusetts 
Institute  of  Technology  show  that  this  mean  value  is 
a  little  low,  but  probably  nearer  the  truth  than  either 
Towne's  or  Rankine's  coefficient.  According  to  these 
later  experiments*  the  value  27  per  cent  was  chosen 
as  being  the  best  under  the  average  conditions  to 
which  an  ordinary  belt  is  subjected  in  practice — allow- 
ing 2^  per  cent  for  slip — and  this  value  has  been  used 
in  calculating  the  widths  given  in  column  9,  the  formula 
used  being 

1000  H.P- 


Reuleaux'  formula,  in  which  0  =  0.28,  instead  of  0.27 
as  here  used,  is 

1 100  H.P. 


V  being  in  feet  per  minute.  The  average  arc  of  con- 
tact, a,  on  the  smaller  pulley  being  equal  to  .95^,  or  a 
little  less  than  180°. 

Upon  consideration  it  will  be  seen  that  the  rule 

800  H.P. 
~F™' 

*  Trans.  A.  S.  M.  E.,  vol.  VH. 


AND    THE   MEASUREMENT  OF  POWER.  I/ 

commonly  used  in  the  machine-shops,  differs  somewhat 
from 

_  looo  H.P. 
i. 06  F~' 

which  takes  into  account  the  arc  of  contact  and  the 
coefficient  of  friction,  the  average  values  a  —  .95 ?r  and 
0  =  .27  being  used. 

Reduced  to  an  equivalent  form  this  equation  becomes 

943^. 

O   =    T+ , 


which  will  give  a  width  of  belt  a  little  greater  than  that 
obtained  by  using  the  shop  rule  referred  to. 

As  the  arc  of  contact  on  smaller  pulley  decreases, 
the  width  of  belt  will  have  to  increase ;  thus  for  an  arc 
of  contact  of  120°  the  width  of  belt  should  be  25  per 
sent  greater  than  that  found  from  the  above  rule. 

As  these  formulas  are  based  on  a  given  thickness  of 
belt,  t,  if  we  increase  this  thickness  the  power  trans- 
mitted ought  to  increase  in  proportion,  and  for  double 
belts  we  should  have  half  the  width  required  for  a 
single  belt  under  the  same  conditions.  With  large 
pulleys  and  moderate  velocities  of  belt  it  is  probable 
that  this  holds  good,  and  this  value  has  been  used  in 
those  cases  in  the  table  where  double  belts  are  em- 
ployed. 

With  small  pulleys,  however,  when  a  double  belt  is 
used  there  is  not  such  perfect  contact  between  the 
pulley-face  and  the  belt — due  to  the  rigidity  of  the 
latter — and  more  work  is  necessary  to  bend  the  belt- 


1 8  D  YNA  MO  ME  TERS 

fibres  than  when  a  thinner  and  more  pliable  belt  is  used. 
The  centrifugal  force  tending  to  throw  the  belt  from 
the  pulley  also  increases  with  the  thickness,  and  for 
these  reasons  the  width  of  a  double  belt  required  to 
transmit  a  given  horse-power  when  used  with  small 
pulleys  is  generally  assumed  not  less  than  seven-tenths 
the  width  of  a  single  belt  to  transmit  the  same  power. 
An  inspection  of  the  fourth  column  shows  that  the 
actual  stress  or  belt-pull  for  single  belting  varies  from 
24  to  135  pounds  per  inch  of  width.  Considering 
these  varying  tensions  and  comparing  the  calculated 
width  with  those  found  in  actual  practice,  we  arrive 
at  the  same  conclusion  previously  reached,  viz.,  that 
the  driving  power  of  a  belt  is  not  directly  determinable 
by  the  use  of  a  formula  unless  the  belt-pull  or  stress  is 
known  for  each  particular  case. 


AND    THE  MEASUREMENT  OF  POWER.  19 


CHAPTER   II. 

FRICTION-BRAKES. 

WE  have  already  stated  that  the  only  satisfactory 
method  of  ascertaining  the  amount  of  power  is  by  the 
use  of  some  form  of  dynamometer — by  which  we  mean 
an  instrument  or  machine  for  measuring  the  power 
exerted  by  a  prime  mover,  or  the  amount  of  power 
consumed  in  driving  a  machine  or  machinery  plant. 

Although  the  engine-indicator  is  an  instrument  for 
measuring  power,  and  is  thus  a  dynamometer,  as  it 
neither  transmits  nor  absorbs  the  power,  its  discussion 
will  not  be  entered  into  in  these  pages.  The  use  of 
the  engine-indicator  in  connection  with  a  new  form  of 
transmission-dynamometer  designed  by  the  writer  will 
be  shown  farther  on. 

Among  the  many  machines  and  devices  for  measur- 
ing power  one  of  the  simplest  is  the  Prony  friction- 
brake  ;  and  but  for  certain  disadvantages  attendant  on 
its  use  it  would  possess  a  superiority  to  all  other  contri- 
vances. 

Primarily  this  consists  of  a  lever  L,  Fig.  I,  connected 
to  a  revolving  shaft  or  pulley  in  such  a  manner  that 
the  friction  induced  between  the  surfaces  in  contact 
will  tend  to  rotate  the  arm  in  the  direction  in  which 
the  shaft  revolves.  This  rotation  is  balanced  by 
weights  P,  hung  in  the  scale-pan  at  the  end  of  the 


20  D  YNAMOME  TERS 

lever.  A  counterpoise  attached  to  the  brake-arm  is 
often  used  in  order  to  balance  it  before  adding  weights 
in  the  scale-pan.  If  not  balanced,  the  weight  of  the 
lever-arm  must  be  ascertained  and  its  moment  added 
to  the  total  moment  of  the  weight  in  order  to  obtain 
an  accurate  measure  of  the  friction.  In  order  to 
measure  the  power  for  a  given  number  of  revolutions 
of  pulley,  we  add  weights  to  the  scale-pan  and  screw 
up  on  bolts  b  b,  until  the  friction  induced  balances  the 


weights  and  the  lever  is  maintained  in  its  horizontal 
position,  while  the  revolutions  of  shaft  per  minute  re- 
main constant.  That  this  measure  of  the  friction  is 
equivalent  to  a  measure  of  the  work  of  the  shaft  will 
be  seen  when  we  consider  that  the  entire  driving 
power  of  the  shaft  is  expended  in  producing  this  fric- 
tion at  the  required  number  of  revolutions  per  minute 
— and  this  driving  power  is  equal  to  the  mechanical 
effect  of  the  shaft  when  running  at  the  same  speed  in 
the  performance  of  useful  work. 

With  the  ordinary  form  of  lever-brake,  in  order  to 
maintain  a  stable  equilibrium  of  the  lever  the  weight 
should  be  supported  on  a  knife-edge  and  act  below 
the  centre  of  the  shaft.  In  this  case,  when  the  weight 


THE  MEASUREMENT  OF  POWER. 


21 


falls  or  rises,  through  any  irregularity  of  the  brake,  the 
lever-arm  is  decreased  or  increased,  and  the  slight 
irregularity  is  overcome  by  a  corresponding  change  of 
moment;  whereas,  if  the  weight  act  above  the  axis, 
any  increase  or  decrease  in  weight  will  cause  it  to  act 
through  a  longer  or  shorter  arm,  as  the  case  may  be, 
and  the  lever  cannot  of  itself  come  back  to  its  hori- 
zontal position.  This  does  not  apply  to  that  form  of 


brake  where  the  force  is  measured  on  a  platform  scale, 
as  it  is  evident  the  lever-arm  is  practically  constant. 
Although  the  construction  of  the  lever  is  of  great  im- 
portance, Mr.  Heinrichs  has  shown  that  the  propor- 
tions of  the  brake  for  different  horse-powers  are  even 
more  important  in  order  to  obtain  uniformity  of  test. 

From  a  number  of  experiments  made  with  a  Prony 
brake  of  the  design  shown  in  Fig.  2,  Mr.  Heinrichs 
gives  the  following  dimensions  as  being  most  suitable 
for  the  horse-powers  designated  :  * 


Mechanics,  1884. 


22 


D  YNA  MOME  7  ~£JfS 


TABLE   III. 
DIMENSIONS  FOR  PRONY  BRAKE. 


Number  of  Revolu- 

Size  of  Brake. 

Diameter 

Brake-pulley. 

Length. 

Width. 

pulley. 

. 

in. 

in. 

From  2  to  5       / 

1200  tO   I8OO 

24 

ii 

4 

horse-power.      | 

7OO  tO  I2OO 

24 

•J 

6 

From  5  to  8       ) 

1200  tO  I60O 

24 

N 

6 

horse-power,      j 

8OO  tO  I20O 

24 

4 

6 

A  regulator  or  dash-pot  attached  to  the  end  of  the 
lever-arm  or  scale-beam  may  be  used  with  the  Prony 
brake — and  other  various  forms  of  dynamometer  in 
which  the  pressure  is  weighed — in  order  to  maintain 
a  more  even  balance  and  to  prevent  vibrations  and 
sudden  shocks  due  to  momentary  slip  of  the  belt  or 
inefficient  lubrication  of  the  brake. 

This  dash-pot  is  generally  in  the  form  of  a  cylinder 
from  4  to  6  inches  in  diameter,  partly  filled  with  oil  or 
water  in  which  a  piston  about  j1^  inch 
less  in  diameter  is  submerged.  This 
piston  will  allow  the  oil  to  pass  freely 
around  it  as  it  rises  or  falls  with  a  slow 
motion,  but  will  oppose  a  resistance  to 
any  sudden  movement.  An  adjustable 
piston  by  which  the  motion  of  the  oil 
can  be  regulated  as  desired  is  sometimes 
an  advantage.  This  can  be  readily 
made  by  turning  two  disks  to  fit  the  bore  of  the  cylin- 
der and  drilling  several  holes  through  both  disks  by 
clamping  together. 


FIG.  3. 


AND   THE  MEASUREMENT  OF  POWER.  2$ 

By  connecting  these  disks  to  a  stem  with  a  shoulder 
and  nut,  any  desired  area  of  opening  between  the  disks 
can  be  obtained  by  turning  one  upon  the  other  and 
tightening  the  nut.  The  piston  should  be  attached  to 
the  scale-beam  by  an  eye  and  pin  so  as  to  move  freely, 
and  the  beam  should  be  balanced  and  adjusted  with 
the  piston  in  place  in  the  liquid  before  beginning  to 
weigh. 

A  dash-pot,  Fig.  3,  used  in  the  Lowell  hydraulic  tests, 
was  made  with  a  thin  disk  of  iron  turned  to  fit  loosely 
in  its  cylinder  ;  six  -f-inch  holes  were  drilled  and  tapped 
in  it  and  fitted  with  brass  thumb-screws,  any  or  all  of 
which  could  be  removed  if  desired  to  allow  a  freer  pas- 
sage Of  the  water  contained  in  the  cylinder ;  the  screw 
being  left  on  the  plate  in  order  to  maintain  the  original 
balance. 

Instead  of  hanging  weights  in  a  scale-pan,  as  in  Fig. 
I,  the  friction  may  be  weighed  on  a  platform-scale;  in 
this  case  the  direction  of  rotation  being  the  same,  the 
lever-arm  will  be  on  the  opposite  side  of  the  shaft. 

A  modification  of  this  brake,  in  which  the  lever  acts 
on  a  platform-scale,  is  that  in  use  in  the  Sibley  College 
Engineering  Laboratory,  and  is  shown  in  Fig.  4.  The 
brake-wheel  is  keyed  to  the  shaft,  and  its  rim  is  pro- 
vided with  inner  flanges  about  two  inches  deep,  which 
form  an  annular  trough  for  the  retention  of  water  to 
keep  the  pulley  from  heating.  A  small  stream  of  water 
constantly  discharges  into  the  trough  and  revolves  with 
the  pulley — the  centrifugal  force  of  the  particles  of 
water  overcoming  the  action  of  gravity ;  a  waste-pipe 
/,  with  its  end  flattened,  is  so  placed  in  the  trough 
that  it  acts  as  a  scoop,  and  removes  all  surplus  water. 


24 


D  YNAMOMETERS 


The  brake  consists  of  a  flexible  metal  strap  to  which 
are  fitted  blocks  of  wood  forming  the  rubbing  surface ; 
the  ends  of  the  strap  are  connected  by  an  adjustable 


FIG.  4. 

bolt-clamp,  by  means  of  which    any  desired   tension 
may  be  obtained. 

The  horse-power  or  work  of  the  shaft  is  determined 
from  the  following : 

Let  W=\vork  of  shaft  in  foot-pounds  per  minute, 

equals  power  absorbed  per  minute  ; 
P=  unbalanced  pressure  or  weight  in  pounds, 

acting  on  lever-arm  at  distance  L ; 
L  —  length  of  lever-arm  in  feet  from  centre  of 

shaft ; 

V '  =  velocity  of  a  point  in  feet  per  minute  at 
distance  L,  if  arm  were  allowed  to  ro- 
tate; 

N  =  number  of  revolutions  per  minute. ; 
H.P.  =  horse-power. 


AND  THE  MEASUREMENT  OF  POWER.  2$ 

Then  will  W=  PV  =  2nLNP. 

PV 
Since  H.P.  —  —  —  ,  we  have 


33000 


If  L  =  —  ,  we  obtain 


271 

NP 


—  =  63.024   inches,  —  practically    5    feet    3   inches  —  a 

value  often  used  in  practice  for  the  length  of  arm. 

It  will  be  noticed  that  neither  the  diameter  of  the 
pulley  nor  the  pressure  and  weight  of  the  friction- 
blocks  on  the  same,  nor  the  coefficient  of  friction 
enter  into  the  formula  for  obtaining  the  horse-power. 
As  previously  noted,  the  friction  induced  between  the 
brake-blocks  and  the  rim  of  the  pulley  tends  to  rotate 
the  brake  in  the  direction  in  which  the  shaft  revolves  ; 
this  rotation  is  counterbalanced  by  the  weight  acting 
upon  the  arm  of  the  brake,  and  when  the  system  is  in 
equilibrium  the  moments  are  equal;  that  is,  if  F  = 
friction  between  blocks  and  pulley  acting  at  radius 
=  Ri  ,  and  P  =  counterbalance  acting  at  distance  L 
from  centre  of  shaft,  we  shall  have 

FR.  =  PL. 

Multiplying  each  member  of  the  equation  by  2nN, 
where  N  =  number  of  revolutions  of  shaft  per  minute, 
we  obtain 

27tN  X  FR,  =  2icNPL  =  W. 


26  D  YNAMOME  TERS 

That  is,  the  work  absorbed  per  minute  by  friction 
equals  the  work  in  foot-pounds  per  minute  at  the  end 
of  the  lever-arm.  And  since  we  have  the  means  of 
obtaining  this  work  Wwhen  the  weight  P  and  arm  L 
are  known,  it  will  readily  be  seen  that  the  friction  and 
radius  of  brake-pulley  do  not  have  to  be  considered  in 
obtaining  the  measure  of  the  power  of  a  rotating  shaft. 
If,  however,  the  coefficient  of  friction,  0,  between  the 
rubbing  surfaces  be  known,  we  may  obtain  from  the 
above  equation  an  expression  for  the  pressure  exerted 
on  the  pulley-rim  by  the  brake  : 

PL 

Let  F  =  —p-  represent  the  force  of  friction  between 

F 

the  surfaces  in  contact  at  the  pulley-rim,  then  ~r  will 

equal  the  pressure  exerted  upon  the  pulley  necessary 
to  produce  the  force  F. 

The  coefficient  of  friction  varies  from  .06  to  .50,  de- 
pending upon  the  different  materials  in  contact  and 
upon  the  lubrication  of  the  surfaces.  Within  certain 
limits,  the  more  perfect  the  lubrication  the  smaller  the 
coefficient  between  any  two  materials. 

A  brake-dynamometer  similar  to  the  one  shown  in 
Fig.  4  is  used  by  the  Westinghouse  Machine  Co.,  in 
testing  their  engines  before  being  sent  out  of  the  fac- 
tory. For  engines  above  125  horse-power  and  under 
250  a  brake-wheel  is  used  which  is  48  inches  in  diameter 
and  24  inches  face,  with  internal  flanges  about  3^  inches 
deep,  carrying  a  stream  of  water  about  2  inches  deep, 
fed  by  a  £-inch  pipe,  the  overflow  being  removed  as 
shown  in  figure  by  means  of  the  scoop-pipe. 

The  rubbing  surface  is  composed  of  28  hard-wood 


AND  THE  MEASUREMENT  OF  POWER.  2/ 

blocks,  oak  or  hickory,  which  are  each  3^  inches  wide, 
spaced  if  inches  apart.  These  blocks  are  lubricated 
with  fat  pork  or  suet,  which  is  packed  in  against  the 
flat  face  of  the  wheel  between  the  blocks.  The  lever- 
arm  is  63^  inches  long. 

For  smaller  engines  a  brake-wheel  48  inches  in 
diameter  by  13  inches  face  is  used,  the  details  being  the 
same  as  in  the  larger  wheel  except  the  brake-arm, 
which  in  this  case  is  shorter,  being  27!  inches  long. 

Even  with  the  sizes  given  a  brake-rim  occasionally 
catches  fire,  the  cooling  water  not  being  sufficient  to 
carry  off  the  heat  quickly  enough. 

The  following  reports  of  tests  made  with  these  brakes 
were  furnished  to  the  writer  through  the  courtesy  of 
the  Westinghouse  Machine  Co.,  both  tests  being  on 
their  Automatic  Compound  Engines  : 

Size  of  engine i6&2?  X  16     8  &  13  X  8 

Initial  steam-pressure 93  96 

Terminal  steam-pressure 13  14 

High-pressure  M.  E.  P 45-37  49-8? 

Low-pressure  M.  E.  P 19-75  22.12 

Indicated  horse-power 205.5  4!'73 

Brake  horse-power 183.48  38.25 

Loss  or  friction , 22.02  3.48 

Percentage  of  loss 10.7  8.3 

Gross  indicated  water-rate 23.95  24.77 

Gross  brake  water-rate 26.83  27.03 

Revolutions  per  minute 249  378 

Brake-load  (pounds) 785  241 

Dead  weight  on  scales 50  n 

Radius  of  brake  (inches) 63^  27! 

Duration  of  test  (minutes) 8  15 

The  arm  of  the  brake  is  often  omitted,  in  which  case 
the  friction  is  induced  either  by  the  use  of  a  flexible 


28  DYNAMOMETERS 

brake-strap  supplied  with  wooden  blocks,  or  simply  by 
the  use  of  a  band  or  ropes  thrown  over  the  pulley. 

For  small  powers  ordinary  leather  belting  from  two 
to  four  inches  wide  is  generally  used,  but  care  should 
be  taken  that  the  belt  is  not  sticky :  a  well-worn  flexi- 
ble belt  free  to  slip  on  the  pulley-face  will  give  the 
most  uniform  results. 

The  belt  should  be  narrower  than  the  pulley-face, 
and,  in  order  to  provide  against  its  slipping 
off  the  rim  sideways,  it  should  be  tacked 
to  three    or    four  light    strips   of    wood 
FIG.  5.        placed    across    the    face    of    the    pulley : 
these   strips  being  cut  out  to  receive  the   pulley-rim 
and  leaving  a  projection  of  about  £  inch  on  each  side 
of  the  rim,  as  shown  in  cross-section  in  Fig.  5. 

In  Fig.  6  is  seen  the  general  arrangement  of  this 
method,  the  belt  being  carried  over  the  pulley  on  the 
motor  to  be  tested  and  one  end  secured  to  the  floor 
by  any  convenient  means.  The  other  end  is  provided 
with  a  scale-pan  or  flat  wooden  box  to  carry  the 
weights.  A  wire  or  stout  cord  attached  to  the  bottom 
of  the  box  and  secured  to  the  floor  will  prevent  the 
accidental  pulling  of  the  box  over  the  shaft  while 
making  the  test.  This  wire  must  necessarily  remain 
slack  when  the  weights  are  in  the  box. 

With  this  form  of  brake  the  power  is  measured  as 
with  the  lever-brake ;  that  is,  the  work,  W,  of  shaft  in 
foot-pounds  per  minute  equals  the  product  of  the 
weight.  P,  in  the  scale-box  multiplied  by  the  velocity, 
V,  in  feet  per  minute  of  the  lever-arm  of  the  weight 
(see  page  24),  which  in  this  case  is  equal  to  the  radius 
of  the  pulley  plus  half  the  thickness  of  the  belt.  If  we 


AND  THE  MEASUREMENT  OF  POWER.  29 

neglect  the  belt-thickness,  the   velocity    V  will  equal 
the  circumferential  velocity  of  the  pulley,  hence 


or  the  horse-power 

27tRNP 
=  "33000    =  °-0001 

where  R  is  radius  of  arm  in  feet,  and  N  =  number  of 


FIG.  6. 


revolutions  per  minute.     If  we  take  radius  of  arm,  r,  in 
inches  we  shall  obtain 


H-p-  =          =  ao0001 


3O  DYNAMOMETERS 

In  working  with  this  belt  brake,  in  order  to  obtain 
accurate  results  the  weights  should  be  so  adjusted  that 
there  shall  be  no  tension  in  the  end  of  the  belt  which 
is  secured  to  the  floor.  A  common  error  is  to  over- 
load the  scale-box  and  create  a  pull  on  the  end  b  which 
will  cause  an  indication  of  power  in  excess  of  its  true 
value.  A  spring-scale  or  balance  interposed  between 
the  end  b  and  the  floor,  as  shown  in  Fig.  7,  will  give 


I    FIG.  7. 

the  amount  of  the  pull,  if  any  exists,  which  pull  should 
be  deducted  from  the  weight  in  the  scale-box. 
It  is  evident  that  the  weight  of  the  spring-scale  should 
be  added  to  the  pull  which  it  indicates  in  order  to  obtain 
the  total  tension  in  the  end  b.  Another  method  is  to 
scrape  the  belt,  thus  causing  a  greater  adhesion  to  the 
pulley-face ;  this  will  pull  the  belt  around  in  the  direc- 


AND    THE   MEASUREMENT  OF  POWER.  3 1 

tion  of  the  arrow,  tending  to  life  the  weight  in  the 
scale-box,  thus  producing  a  slackness  at  the  end  secured 
to  the  floor.  With  care  in  the  weighting,  if  sufficiently 
small  weights  are  provided  there  need  be  little  or  no 


tension  at  b.  A  3-inch  belt  over  a  24-inch  pulley  run- 
ning at  .200  revolutions  per  minute,  with  a  wreight  of 
50  pounds  in  the  scale-box,  will  measure  about  2  horse- 
power 


32  D  YNAMOME  TERS 

For  larger  powers  the  brake-strap  is  lined  with 
wooden  blocks  and  encircles  the  pulley,  the  friction 
being  measured  either  by  attaching  weights  to  a  hook 
or  scale-pan  and  screwing  up  on  an  adjusting  bolt  which 
brings  the  two  ends  of  the  strap  together ;  or  a  spring 
balance  is  used  in  connection  with  the  adjusting  screw, 
as  shown  in  Fig.  8. 

In  the  Brauer  compensating  brake,  the  band  which 
encircles  the  pulley  is  of  thin  rolled  iron  when  the 
pulley-rim  is  flat ;  wire  ropes  are  used  for  a  grooved 
pulley. 

For  small  forces  Mr.  Gisbert  Kapp  has  advanta- 
geously employed  the  arrangement  represented  in  Fig. 
9.  The  brake-cord,  which  embraces  half  the  pulley 


FIG.  9. 

circumference,  is  attached  at  E  on  a  level  with  the 
knife-edge  of  the  scale-beam,  and  at  D  in  a  point 
somewhat  below,  so  that  the  lever-arm  of  D  is  in- 


AND    THE  MEASUREMENT  OF  POWER. 


33 


creased  while  that  of  E  is  diminished,  thus  forming  a 
compensating  device.  The  spring  S  and  nut  N  allow 
an  adjustment  of  the  tension  in  the  cord  after  the 
scale-pan  is  weighted. 

The  brake  recommended  by  the  Royal  Agricultural 
Society,*  designed  by  Mr.  C.  E.  Amos  and  Mr.  Appold, 


is  somewhat  similar  to  those  already  described,  but,  as 
will  be  noticed,  Fig.  10,  this  brake  is  provided  with  a  self- 
acting  system  of  levers  which  are  arranged  to  adjust 
the  tension  in  order  to  compensate  for  the  variations 
in  the  moment  of  friction. 

*  Proc.  British  Inst.  C.  E.,  vol.  xcv,  1888-89. 


34  D  YNA  MOME  '2  'ERS 

In  this  brake  the  strap  is  made  in  two  parts  to  which 
blocks  of  wood  are  secured,  and  at  a  convenient  point 
the  two  portions  are  joined  by  a  right-and-left-hand 
adjusting  screw. 

The  other  ends  of  the  strap  are  jointed  to  a  double 
swinging  lever  in  such  a  manner  that  the  radii  of  the 
two  ends  of  the  strap  from  the  centre  of  oscillation  of 
the  lever  are  unequal. 

If,  through  deficiency  of  lubrication  or  other  causes, 
the  wheel  should  tend  to  carry  the  strap  around  with 
it  in  the  direction  of  the  arrow,  the  greater  radius  of 
the  end  nearer  the  weight  would  effect  a  loosening  of 
the  strap  and  a  diminution  of  the  friction  ;  whereas  if 
the  friction  is  momentarily  insufficient  to  sustain  the 
weight,  it  will  in  falling  tighten  the  strap,  and  thus 
maintain  automatically  a  fairly  constant  moment. 

This  form  of  brake,  like  that  of  Appold,  can  only  be 
used  for  measuring  small  horse-powers,  unless  we  take 
into  account  the  reaction  at  the  point  of  suspension  of 
the  lever. 

So  long  as  the  friction  between  the  wooden  blocks 
and  wheel  is  such  that  the  weight  of  the  brake-strap 
and  suspended  weight  is  sufficient,  at  the  required 
speed,  to  carry  the  load  without  tightening  the  adjust- 
ing screw  to  any  extent,  the  lever  does  not  affect 
the  results — the  conditions  being  similar  to  those  which 
would  obtain  if  the  brake  were  without  compensating 
lever,  and  the  strap  so  slack  that  the  bottom-blocks 
barely  touch  the  wheel.  That  the  resultant  of  the  ten- 
sions in  the  brake-band  resolved  along  the  lever  affects 
the  measure  of  the  power  can  be  shown  by  means  of 
the  following  figure  (u). 


AND    THE  MEASUREMENT  OF  POWER. 


35 


Let  the  lever-ECD  be  in  the  position  shown,  and  the 
system  in  equilibrium.  The  tensions  of  the  brake- 
blocks  on  the  lever  towards  the  right  at  C,  and  left  at 
D,  are  represented  in  the  figure  by  Tl  and  Ty  On  the 
other  hand,  the  reactions  of  the  lever  on  the  brake- 
blocks  are  Tl  towards  the  left  at  C,  and  Ty  towards  the 
right  at  D\  then,  since  there  is  equilibrium  in  the  sys- 


FlG.  IT 

tern,  the  algebraic  sum  of  the  moments  taken  about  the 
centre  of  shaft  must  equal  zero. 

The  resultant  of  the  forces  Tl  and  Tt ,  which  we  may 
call  Q,  must  pass  through  the  point  of  suspension,  £,  of 
the  lever.  Resolving  this  force  Q  into  its  vertical  and 
horizontal  components  acting  at  the  point  E,  which  is 


36  D  YNAMOME  TEKS 

directly  under  the  centre  of  the  shaft  or  centre  of 
moments,  we  have  the  moment  of  the  vertical  compo- 
nent equal  to  zero.  Calling  the  horizontal  component 
h,  and  the  vertical  component  v,  we  have  the  sum  of 
the  moments  about  the  centre  of  rotation  : 

PR  —  FR,  -  hr  -  vo  =  o, 


in  which  P  is  the  weight  acting  on  brake  at  radius  R  ; 
F  is  the  friction  between  brake-blocks  and  rim  of  pulley 
acting  at  radius  Rl  ;  and  //  is  that  component  of  the 
reaction  at  the  point  of  support  of  the  lever  which  tends 
to  produce  a  rotation  about  the  centre  of  shaft  ;  its 
lever-arm  =  r. 

Since  FRl  —  PR  —  hr,  we  have 

2?rNFRl  =  27tN(PR  -  hr)  ; 

that  is,  the  work  absorbed  by  friction  equals  the  work 
of  the  shaft  in  foot-pounds  per  minute  (when  Rt  ,  R,  and 
r  are  in  feet,  and  N  =  revolutions  per  minute),  or,  as 
previously  found, 

W=  2nN(PR-hr\ 
and 

horse-power  =  ---  (PR  —  hr). 

The  amount  of  the  force  h  is  best  obtained  by  the 
use  of  a  spring-balance.      With  a  high  coefficient  of 


AND    THE  MEASUREMENT  OF  POWER. 


37 


friction  the  force  h  may  be  small,  and  might  be  disre- 
garded in  approximate  measurements,  but  in  every  case 
where  accuracy  is  desired  its  moment  must  be  con- 
sidered. 

Ropes  used  as  brake-straps  have  given  very  satisfac- 
tory results. 


Prof.  Andrew  Jamieson,  of  the  Glasgow  College  of 
Science  and  Arts,  states  that  he  prefers  a  rope  brake  to 
any  one  of  the  numerous  forms  which  he  has  tried, 
and  believes  that  it  could  be  adopted  for  large  powers 
and  for  long  continuous  runs,  for  the  following  reasons  : 

"  It  could  be  constructed  on^very  short  notice  from 
materials  always  at  hand  in  every  factory,  and  at  very 


.'J79424 


38  D  YNA  MO  ME  TERS 

little  expense.  It  is  so  self-adjusting  that  no  accurate 
fitting  is  required.  It  can  be  put  on  and  taken  off  in  a 
moment ;  is  very  light  and  of  small  bulk.  It  needs 
little  or  no  attention  for  lubrication.  The  back-pull 
registered  by  the  spring-balance  is  steady,  and  might 
be  made  a  minimum  by  properly  adjusting  the  weight. 
For  larger  powers  only  more,  or  larger,  or  flatter  ropes, 
or  a  larger  brake-wheel,  would  be  required." 

Fig.  12  represents  a  rope-brake  used  by  Prof.  Jamie- 
son  to  indicate  a  gas-engine  of  fifteen  brake  horse- 
power. In  this  test  the  diameter  of  ropes  was  0.6  inch, 
working  over  a  5-foot  fly-wheel. 

The  following  are  some  of  the  conditions  under  which 
the  test  was  made  :  * 

Mean  revolutions  of  brake-wheel  per  minute 205 

Weight,  P,  in  Ibs 157 

Mean  back-pull  on  balance,  in  Ibs 4 

Mean  brake  H.  P.  during  two  hours'  run 1 5.23 

Gas-consumption  per  brake  H.  P.  in  cu.  ft.  per  hr.  24.3 
"    indie.       "  "  "        18.9 

More  recently  Prof.  Jamieson  has  used  the  forms  of 
rope-brake  shown  in  Fig.  13.  These  are  of  the  same 
kind  employed  in  the  trials  of  gas-engines  under  the 
auspices  of  the  Society  of  Arts,  London,  and  give  much 
more  satisfactory  results  than  any  other  form  of  brake 
hitherto  devised  for  light  work.  The  substitution  of 
the  spring-balance  in  the  right-hand  figure  for  the 
weight  shown  at  the  left  of  the  figure  is  a  decided  ad- 

*Sce  paper  by  W.  W.  Beaumont  in  Proc.  British  Tnst.  C.  E., 
1888-9;  also  Jamieson's  Steam  and  Steam-engines  (London,  1890). 


AND    THE  MEASUREMENT  Of  POWER.  39 


FIG.  13. — Two  FORMS  OF  ROPEB-RAKB  USED  BY  PROF.  JAMIESON. 


40  D  YNA  MOME  TERS 

vantage,  since  by  the  use  of  two  spring-balances  of 
different  periods  of  oscillation  the  "  hunting"  action  of 
the  brake  is  effectually  minimized,  enabling  observa- 
tions to  be  taken  with  great  precision.  To  obtain  the 
brake-load  it  is  only  necessary  to  add  the  weight  of  the 
hanging  part  of  the  lower  balance  to  its  own  reading, 
and  subtract  from  this  sum  the  back-pull  as  registered 
by  the  reading  of  the  upper  scale. 

This  form  of  brake  deserves  to  be  better  known  ;  for 
with  it  no  lubrication  whatever  is  required,  and  con- 
tinuous runs  of  any  desired  length  of  time  may  be 
carried  out  without  any  fear  of  overheating  or  requir- 
ing to  stop  for  adjustment. 

With  this  brake  Prof.  Jamieson  conducted  a  five- 
hour  continuous  test  of  Brown's  Rotary  Engine,*  and 
obtained  for  speeds  varying  from  560  to  600  revolu- 
tions per  minnte  an  average  brake  horse-power  of 
20.78.  As  the  brake-wheel  used  was  4  feet  in  diame- 
ter it  will  be  seen  that  the  average  surface  velocity 
was  nearly  7300  feet  per  minute — a  very  unsatisfactory 
speed  for  friction-brakes. 

An  interesting  form  of  brake-dynamometer  invented 
by  M.  Rappard,  modified  in  order  to  adapt  its  use  to 
large  forces  and  high-speed  machinery,  is  thus  described 
in  a  recent  issue  of  La  Lumiere  Electrique :  f 

"  One  of  these  improvements  consists  in  the  substitu- 
tion, for  the  rubbing  surfaces,  of  linen  bands  secured  to 
metallic  straps,  instead  of  the  ordinary  belts  usually 
employed.  In  this  way  a  composition  belt  is  obtained 

*  Trans.  Inst.  Engineers  and  Shipbuilders  in  Scotland,  Nov.  1891. 
f  August  i,  1891. 


AND    THE  MEASUREMENT  OF  POWER.  4! 

which  is  entirely  inextensible,  very  strong  and  perfectly 
free  to  allow  water  to  pass  to  cool  the  surfaces. 

"A  strip  of  brass  .08  inch  thick  covered  with  bands 
of  linen  .04  inch  thick  constitutes  a  very  desirable  form 
of  belt  for  this  work. 

"  It  is  by  the  use  of  this  new  form  of  inextensible 
strap  that  M.  Rappard  has  been  able  to  construct  the 
machines  represented  by  Figs.  14  to  16. 

The  apparatus  represented  by  Fig.  14  consists — 

"  ist.  Of  a  brake  shaft  connected  by  a  universal 
joint  to  the  motor  to  be  tested. 

"  2d.  Of  a  drum  mounted  mid-length  of  the  brake- 
shaft,  and  of  two  loose  pulleys  placed  on  each  side  of 
the  drum,  upon  the  hubs  of  which  the  arms  of  a  forked 
balance-yoke  are  supported. 

"  3d.  Of  three  metallic  straps,  two  for  the  loose  pulleys 
and  the  other  for  the  drum :  this  last,  which  produces 
the  friction,  is  covered  with  a  band  of  linen ;  from  the 
forked  yoke  to  which  it  is  attached  this  strap  passes 
over  the  drum  and  descends  vertically  to  the  lower 
cross-bar  of  the  frame. 

"  The  two  other  straps,  also  attached  to  the  forked 
yoke,  envelop  the  lower  surface  of  the  loose  pulleys, 
from  which  they  rise  vertically  and  are  attached  to  the 
upper  cross-bar  of  the  frame. 

"  This  vertical  frame  of  wood  (it  would  be  better  to 
construct  it  in  part  of  wrought-iron  pipe)  carries  at  top 
and  bottom  two  strong  cross-bars,  through  which  pass 
the  bolts  which  receive  the  ends  of  the  straps. 

"  These  bolts  are  for  regulating  the  tension  of  the 
straps  so  as  to  produce  the  necessary  friction  to  balance 
the  load  of  the  brake. 


DYNAMOMETERS 


"  The  whole  apparatus  is  suspended  by  a  chain  which, 
after  passing  over  a  pulley  rigidly  supported  above  the 


frame,  descends  vertically  and  is  attached  to  the  lower 
bar  of  the  frame,  as  shown. 


AND    THE   MEASUREMENT  OF  POWER.  43 

"This  arrangement  is  used  to  insure  an  equal  rolling 
and  unrolling  of  the  belts  on  the  pulleys  and  drum,  in 
order  to  maintain  a  constant  load  on  the  brake  not- 
withstanding the  vertical  movement.  The  weight  of 
the  frame  and  the  brake-load  are  carried  upon  a  rod 
situated  in  the  centre  of  the  vertical  portion  of  the 
chain. 

"  There  will  often  be  an  advantage  in  placing  the 
apparatus  horizontally;  in  this  case  the  plane  of  the 
bands  is  placed  tangentially  to  the  upper  part  of  the 
drum,  the  horizontal  motion  being  obtained  by  means 
of  small  friction  rollers  placed  under  the  frame.  At 
each  end  of  the  frame  there  is  a  chain  which,  after 
being  stretched  horizontally,  passes  under  the  pulley  at 
an  angle  and  descends  vertically  to  the  floor.  The 
chains  should  be  long  enough  so  that  they  do  not  leave 
the  floor  whatever  the. motion  of  the  frame. 

"  The  brake-load  is  placed  upon  that  one  of  the  two 
chains  which  is  connected  to  the  cross-bar  of  the  frame 
to  which  are  attached  the  bands  from  the  loose  pulleys. 

"  Fig.  15  is  another  arrangement  of  the  Rappard  bal- 
ance-dynamometer which  permits  placing  the  brake- 
shaft  nearer  the  floor.  The  centre  strap,  covered  with 
canvas,  and  which  forms  the  rubbing  surface,  passes 
downwards  and  under  a  guide-pulley,  thence  upwards 
to  the  rod  which  receives  the  weights. 

"  The  two  other  bands,  after  passing  under  the  loose 
pulleys,  ascend,  and  are  carried  over  guide-pulleys, 
thence  downwards,  and  are  attached  to  the  extremities 
of  a  short  beam,  the  centre  of  which  receives  the  eye  of 
the  rod  which  carries  the  load. 

"  Tension  in  the  straps  is  obtained  by  means  of  two 


44 


D  YNAMOME  TERS 


screws  and  nuts  which  allow  the  shaft  of  the  guide-pul- 
leys to  be  raised  or  lowered. 

"  The  water  necessary  for  cooling  the  straps  of  the 


FIG.  15. 


brake  instead  of  falling  upon  the  exterior  surface,  is 
delivered  to  the  interior  of  the  drum  by  two  small  pipes 
passing  between  the  drum  and  the  two  loose  pulleys. 
The  water  is  retained  in  the  interior  of  the  drum  by 


AND    THE  MEASUREMENT  OF  POWER. 


45 


two  narrow  flanges,  and  is  distributed  over  all  the  sur- 
face centrifugally;  perforations  across  the  face  of  the 
drum  allow  the  water  to  lubricate  the  strap. 

"  These  automatic-balance-brakes  permit  very  accu- 
rate results,  for  there  is  only  the  friction  of  the  brake- 
shaft  bearings  to  be  deducted  from  the  total  measure  of 


the  work  ;  however,  this  friction  is  very  small,  since,  on 
an  average,  it  does  not  rise  above  one  fourth  per  cent 
of  the  total  work  in  an  apparatus  measuring  50  horse- 
power. 

"  Still  this  cause  of  error  can  readily  be  overcome  if 
desired,  by  mounting  on  friction  rollers.  In  this  case 
the  brake-shaft  bearings  are  replaced  by  the  lengthened 
hubs  of  the  loose  pulleys,  which  are  supported  by  four 
pairs  of  rollers  as  shown  in  Fig.  16;  as  will  be  noticed, 
the  hubs  of  the  loose  pulleys  do  not  revolve,  and  only 
follow  the  angular  displacement  of  the  forked  yoke 
caused  by  the  variations  of  friction." 

If  we  wish  to  determine  the  horse-power  of  a  verti- 
cal shaft — for  instance  that  of  a  turbine — by  means  of 
a  friction-brake,  we  can  no  longer  suspend  the  weight 
directly  from  the  bar  or  lever,  but  must  insert  a  bent 
lever,  so  that  the  vertical  direction  of  the  weight  may 
be  converted  into  a  horizontal  force. 


46  D  YNAMOME  TERS 

Fig.  17  represents  a  friction-brake  for  a  vertical 
shaft  which  w#s  used  by  Francis  in  his  Lowell  hydraulic 
experiments  in  testing  a  i5O-horse-power  turbine.  The 
brake-wheel  rim  A  is  of  cast-iron  5^  feet  in  diameter 
and  24  inches  width  of  face.  This  rim  is  3  inches 
thick,  and  is  cast  with  internal  lugs  which  permit  it 


to  be  bolted  to  a  spider  keyed  to  the  turbine  shaft 
D,  provision  being  made  for  a  slight  expansion  between 
the  end  of  the  arms  and  the  brake-rim,  which  is  flanged 
to  receive  the  brake-shoes.  The  brakes,  E  and  F,  are 
of  maple,  and  are  tightened  by  two  2-inch  square  bolts  ; 
one  of  the  brake-arms,  F,  is  connected  to  the  swinging 
lever,  K,  by  means  of  the  rod  KL,  as  shown.  From  one 
end  of  this  lever  the  scale-pan  is  hung,  and  to  the  other 


AND    THE  MEASUREMENT  OF  POWER.  4? 

end  is  connected  a  hydraulic  regulator,  N  (see  Fig.  3), 
which  consists  of  an  iron  plate,  half  an  inch  thick,  turned 
-jig-  inch  less  than  diameter  of  cylinder,  free  to  move 
up  and  down  in  a  cylinder  filled  with  water,  so  that 
it  acts,  as  previously  noted,  as  a  moderator  in  con- 
trolling any  sudden  vibrations  of  the  lever-arm.  The 
brake  is  cooled  by  means  of  a  forked  pipe,  R,  which 
throws  jets  of  water  against  the  wheel,  the  quantity  of 
cooling  water  being  about  .17  cubic  feet  per  minute. 
When  running  slow  the  lubrication  was  with  linseed 
and  resin  oil ;  water,  however,  was  preferred  for  the 
faster  speeds — about  60  revolutions  per  minute. 

Mr.  Samuel  Webber,  in  1884,  had  occasion  to  test 
a  large  turbine  at  Augusta,  Ga.,  and  for  this  pur- 
pose  had  a  brake  made  similar  in  appearance  to  the 
one  shown  in  Fig.  4,  page  24,  but  arranged  hori- 
zontally with  a  bent  lever  like  the  one  just  shown. 
In  this  brake  the  friction-pulley  was  7  feet  in  diameter 
and  24  inches  face.  The  brake-lever  was  of  oak,  16 
inches  square,  reaching  15.91  feet  from  the  centre  of 
shaft  to  the  point  of  connection  with  the  bent-lever 
scale-beam,  which  latter  had  a  leverage  of  two  to  one 
to  reduce  the  amount  of  weights  to  be  handled. 
Lubrication  was  supplied  by  strong  soap-suds  fed 
from  three  large  cans  placed  at  intervals  around  the 
brake.  Besides  this  a  thin  jet  of  water  was  thrown 
upon  the  brake  through  a  flattened  nozzle. 

The  apparatus  worked  perfectly,  and  a  steady  test 
was  obtained  of  475  H.  P.  at  76  revolutions  of  the 
wheel  per  minute. 

This  is  probably  the  heaviest  test  of  a  single  motor 
ever  made  with  a  brake. 


48  DYNAMOMETERS 

The  strap  of  the  brake  was  made  of  boiler-iron  lined 
with  blocks  of  soft  wood,  and  the  pulley  had  deep 
flanges,  so  that  the  brake  set  into  it  like  a  saddle. 
The  iron  clamp  was  in  two  pieces  hinged  together  at  a 
point  opposite  the  adjusting  bolt. 

In  connection  with  this  brake  Mr.  Webber  used  a 
hydraulic  regulator  for  the  scale-beam,  the  cylinder  of 
which  was  18  inches  diameter  and  the  piston  i/|  inches. 

In  using  any  form  of  friction-brake,  if  the  surface  in 
contact  with  the  pulley  be  too  large,  it  will  be  found 
that  a  considerable  weight  may  be  added  to  the  scale- 
pan  without  materially  altering  the  position  of  the 
lever-arm ;  but  if,  on  the  other  hand,  this  rubbing 
surface  be  too  small,  the  resulting  friction  will  show 
great  irregularity — probably  on  account  of  insufficient 
lubrication — the  jaws  being  allowed  to  seize  the  pulley, 
thus  producing  shocks  and  sudden  vibrations  of  the 
lever-arm.  The  material  in  contact  with  brake-pulley, 
no  doubt,  enters  largely  into  the  question  of  smooth 
running,  especially  if  the  lubrication  be  not  of  the  best. 
Soft  woods,  such  as  bass,  plane-tree,  beech,  poplar,  or 
maple,  are  generally  to  be  preferred  to  the  harder  woods 
for  brake-blocks.  Old  leather  belting,  secured  to  wooden 
blocks,  forms  a  good  rubbing  surface,  provided  the 
leather  is  not  sticky  or  gummy,  and  maintains  a  very 
regular  motion  of  the  brake  if  properly  lubricated. 

For  high  speeds  and  small  powers  the  writer  has 
found  strong  soap-suds  very  efficient  for  this  purpose. 
A  convenient  method  of  supplying  the  lubricant  to 
small  brakes  is  to  place  a  large  can,  provided  with  a 
pet-cock,  directly  above  the  brake,  allowing  the  soapy 
water  to  trickle  down  two  or  more  wires  which  lead  to 


AND    THE  MEASUREMENT  OF  POWER. 


49 


the  pulley-surface.  A  trough  and  shield  can  be  suit- 
ably arranged  to  catch  the  excess  of  water  thrown  from 
the  pulley. 

For  light  tests  Mr.  Webber  has  found  that  cork  gives 
a  very  good  rubbing  surface. 


Babbitt  metal  has  also  been  used  for  this  purpose — 
the  pulley  being  grooved  and  the  Babbitt  shoes  cast 
to  fit  it.  There  is  no  doubt  that  this  material  would 
give  excellent  results  as  a  brake-rubbing  surface  if 
properly  lubricated. 


$O  D  YNAMOME  TERS 

Self-cooling  brakes,  Fig.  18,  where  both  the  rim  of 
the  pulley  and  the  brake-strap  were  hollow,  with  a 
stream  of  cold  water  flowing  through  them,  were 
used  by  Mr.  Emerson  at  Lowell  in  1869,  oil  being 
used  on  the  metallic  rubbing  surfaces  as  the  lubri- 
cant. In  this  brake  the  wheel  B  is  made  of  cast-iron, 
and  the  friction-band  of  composition  or  gun-bronze,  the 
hollow  band  being  supplied  with  water  from  the  out- 
side, while  the  rim  of  pulley  is  kept  cool  by  means  of 
water  which  enters  the  hub  and  is  delivered  through 
the  hollow  arms  to  the  rim. 

Mr.  W.  W.  Beaumont,  in  his  excellent  paper  on 
"  The  Friction-brake  Dynamometer,"  previously  re- 
ferred to,  has  given  a  formula  by  means  of  which  the 
relative  capacities  of  brakes  can  be  compared,  judging 
from  the  amount  of  horse-power  ascertained  by  their 
use: 

If  W=  width  of  rubbing  surface  on  brake-wheel  in 

inches ; 
V=  velocity  of  point  on  circumference  of  wheel 

in  feet  per  minute  ; 
K=  coefficient, — then 


"  ~H.P: 

The  average  of  three  brakes  cited  by  Mr.  Beaumont 
gives  the  value  of  K  as  860. 

In  Table  IV  is  given  a  number  of  tests  and  the  size 
of  brake  used,  from  which  the  value  of  A"  has  been  cal- 
culated,  as  shown  in  the  last  column.  These  figures 


AND    THE  MEASUREMENT  OF  POWER. 


have  been  collected  from  various  sources  and  represent 
varied  practice. 


TABLE   IV. 
CAPACITY  OF  FRICTION-BRAKES. 


R.P.M. 

Brake- 

pulley. 

Length  of 

Horse- 
power. 

Brake- 
puliey. 

Face  ir 
inches. 

Dia    in 
feet. 

arm  in 
inches. 

Design  of  Brake. 

Value 
of  K. 

21 

150 

7 

5 

33 

Royal    Ag.    Soc.,    com- 

pensating   

785 

19 

148.5 

7 

5 

33-38 

McLaren,  compensating 

858 

20 

146 

7 

5 

32.19 

McLaren,    water-cooled 

and  compensating.  .  . 

802 

40 

180 

10.5 

5 

32 

Gatrett,       water-cooled 

and  compensating.  .  . 

741 

33 

IKO 

10.5 

5 

32 

Garrett,       water-cooled 

and  compensating. 

749 

150 

150 

10 

9 

Schoenheyder,       water- 

cooled  

282 

24 

142 

12 

6 

38.31 

Balk,  compensating.  .  .  . 

1385 

180 

100 

24 

5 

I26.I 

Gately  &  Kletsch,  water- 

cooled  

209 

475 

76.2 

24 

7 

15.  gift. 

Webber,  water-cooled.  . 

84.7 

125) 

2CQ  ( 

290) 

2CO    C 

24 

4 

63 

Westinghouse,       water- 
cooled 

465 

*y  i 

40  i 

I2C   C 

•*D°  ) 
322  ) 
2QO  f 

'3 

4 

*7l 

VVestinghouse,       water- 
cooled 

847 

A*D   J 

^yw  j 

By  referring  to  the  table  it  will  be  seen  that  the 
above  calculations  for  eleven  brakes  give  values  of  K 
varying  from  84.7  to  1385  for  actual  horse-powers 
tested,  the  average  being  K  =  655.  By  a  comparison 
of  the  sizes  and  speeds  given  by  Mr.  Heinrichs  (see 
Table  II),  K  is  found  to  average  895  for  small  horse- 
powers varying  from  2  to  8.  From  the  nature  of  the 
device,  these  latter  brakes  are  not  water-cooled. 


52  D  YNA  MO  ME  TERS 

In  the  Gately  &  Kletsch  water-cooled  brake  (for  de- 
scription of  which  see  article  by  Prof.  R.  H.  Thurston 
in  Jour.  Franklin  Inst.,  April  1886)  the  wheel  was 
designed  to  measure  540  horse-power,  but  it  does  not 
appear  to  have  been  used  to  indicate  more  than  180 
horse-power. 

For  this  number  K  =  209.  In  the  Schoenheyder 
water-cooled  brake  K  =  282  ;  in  the  large  Westing- 
house  brake  K  varied  from  288  to  709  for  actual  horse- 
powers tested,  averaging  465. 

For  the  smaller  Westinghouse  brake,  K  averaged 
847,  which  seems  to  be  the  only  case  in  which  the 
value  of  the  coefficient  for  non-compensating  brake  ex- 
ceeds that  ascertained  for  compensating  brakes.  The 
average  value  of  K  for  the  several  water-cooled  non- 
compensating  brakes  is  377,  and  for  the  compensating 
brakes  ^=853.  Neglecting  the  extreme  value  as 
given  for  the  Balk  brake,  K  will  equal  762. 

From  these  deductions  it  would  appear  that  when 
the  brake-strap  is  provided  with  some  form  of  compen- 
sating device  (as,  for  instance,  that  shown  in  Fig.  10)  by 
which  a  self-acting  adjustment  of  the  tension  of  the 
strap  is  supposed  to  maintain  a  nearly  constant  moment 
of  friction,  the  rubbing  surface  is  generally  greater  than 
when  such  device  is  not  employed.  Instead,  therefore, 
of  assuming  an  average  coefficient  of  860,  the  writer 
would  propose  the  following  : 

K—  400  for  water-cooled  brake  non-compensating  ; 
K  =  750  for  water-cooled  brake  compensating  ; 
^=900  for   non-cooled  brake  with  or  without  com- 
pensating device. 


AND    THE  MEASUREMENT  OF  POWER.  53 

For  metal  brake-shoes  the  value  of  K  could  prob- 
ably be  much  less,  as  the  radiation  of  heat  from  the 
metallic  surfaces  would  be  greater. 

From  the  above  values  of  K  the  width  of  brake- 
wheel  can  be  obtained  for  the  different  types  : 


_ 


V 


V 

in  which,  as  before,  W  '=  width  of  bearing  surface  in 
inches  on  pulley,  and  V  •=•  velocity  of  a  point  on  cir- 
cumference of  pulley  in  feet  per  minute. 

In  the  different  forms  of  Prony  and  friction  brake,  it 
is  evident  that  as  the  work  of  the  shaft  is  all  spent  in 
overcoming  the  resistance  due  to  friction,  no  useful 
work  is  done.  The  friction-brake  is  thus  an  absorbing 
dynamometer. 


54 


D  YNAMOME  TERS 


CHAPTER   III. 

ABSORPTION-DYNAMOMETERS. 

ANOTHER  form  of  absorbing  dynamometer  is  that  de- 
signed by  Prof.  C.  B.  Richards,  of  the  Sheffield  Scien- 
tific School  of  Yale  University.  It  consists  of  a  tank, 
AB  (Fig.  19),  within  which  two  paddle-wheels  revolve 


Oil  Supply 


FIG.  ,9. 

in  oil,  thus  producing  a  resistance  and  a  tendency  to 
rotate  the  whole  tank,  which  is  mounted  on  friction- 
rollers.  This  tendency  to  rotate  is  measured  by  the 
lever-arm  acting  on  a  platform-scale.  By  means  of  the 
valve  v  the  oil  in  the  tank  can  be  allowed  to  circulate 
with  greater  or  less  freedom  ;  by  closing  the  valve  a 


AND   THE  MEASUREMENT  OF  POWER.  55 

pressure  is  brought  to  bear  on  the  oil  in  the  tank,  so 
that  the  resistance  to  the  rotation  of  the  inner  wheels 
thus  becomes  a  drag  on  the  driving  power ;  when  the 
maximum  resistance  is  obtained  without  decreasing 
the  number  of  revolutions  per  minute  of  the  shaft,  the 
force  of  resistance,  measured  on  the  scale-beam,  will 
enable  us  to  calculate  the  horse-power  consumed.  In 
order  to  prevent  any  change  of  temperature  in  the  oil, 
a  constant  stream  of  water  is  discharged  onto  the  tank 
through  a  perforated  pipe,  P,  above  it.  Beneath  the 
tank  proper  a  metal  receiver,  R,  catches  the  water, 
which  is  then  carried  off  by  the  waste-pipe  W,  shown 
at  the  bottom  of  the  receiver. 

Part  of  the  tank  AB,  and  also  of  the  outside  receiver 
R,  is  torn  away  in  the  figure,  in  order  to  show  more 
clearly  the  circulation  of  oil  and  position  of  the  paddle- 
wheels.  One  of  these  latter  is  mounted  on  the  pulley- 
shaft,  and  has  the  same  direction  of  rotation  as  the 
belt-pulley ;  the  other  is  driven  by  a  gear  (not  shown), 
and  revolves  in  the  opposite  direction.  A  casing  at 
each  end  of  the  tank  fits  close  to  the  paddle-wheels, 
the  blades  of  which  roll  on  each  other.  In  this  re- 
spect the  internal  arrangement  is  similar  to  that  of 
various  rotary  engines  and  blowers.  In  order  that 
there  should  be  a  minimum  amount  of  vibration  of  the 
scale-beam  while  weighing  the  pressures,  a  rod  and 
dash-pot  were  used — the  latter  being  supported  by  an 
arm  attached  to  the  side  of  the  scales. 

The  size  of  this  dynamometer  was  30  X  14  X  18 
inches,  and  would  measure  from  ^  to  14  horse-power. 

With  this  apparatus,  as  with  the  Prony  brake,  it  will 
be  seen  that  an  absorbing  dynamometer  cannot  be 


56  D  YNAMOME  TERS 

used  to  determine  the  power  which  is  actually  trans- 
mitted to  a  machine ;  it  can  only  measure  the  power 
which  is  produced  in  circumstances  as  similar  as  pos- 
sible to  those  under  which  the  machine  is  operated ; 
and  this  power  is  assumed  equivalent  to  that  con- 
sumed by  the  machine.  About  the  year  1873,  Prof. 
Richards  used  this  principle  of  measuring  the  tendency 
of  the  belt  to  rotate  a  body  about  its  axis,  and  de- 
signed a  stand  or  cradle  upon  which  the  machine  itself 
was  suspended  on  trunnions.  When  the  machine  to 
be  tested  was  put  in  motion,  its  tendency  to  rotate 
thus  became  a  measure  of  the  resistance. 

This  same  principle  was  introduced  by  Prof.  Brack- 
ett,  of  Princeton,  a  number  of  years  later,  in  his 
cradle-dynamometer,  which  is  now  very  generally  and 
successfully  used  in  testing  dynamos  and  electric  mo- 
tors. 

A  little  consideration  will  show  that  the  cradle- 
dynamometer  measures  the  actual  power  transmitted 
to  the  machine  or  developed  by  the  motor,  and  is  thus 
a  transmitting  dynamometer.  As  such  it  will  be  con- 
sidered subsequently. 

An  absorption-dynamometer,  by  which  also  any 
desired  load  can  be  maintained  on  the  engine,  is  the 
invention  of  Prof.  Alden,  of  Worcester.  This  dyna- 
mometer is  essentially  a  friction-brake  in  which  the' 
pressure  causing  the  friction  is  distributed  over  a  com- 
paratively large  area,  thus  giving  a  low  intensity  of 
pressure  between  the  rubbing  surfaces. 

This  friction  is  produced  by  the  pressure  of  water 
from  the  city  pipes  acting  upon  two  copper  plates  in 
contact  with  a  smooth  cast-iron  disk  keyed  to  the  shaft 


AND    THE  MEASUREMENT  OF  POWER. 


which  revolves  in  a  bath  of  oil  between  the  plates. 
These  latter  are  secured  by  a  water-tight  joint  to  a 
casing  which  does  not  revolve,  and  to  which  is  bolted 
a  lever-arm  carrying  weights  as  in  an  ordinary  Prony 
brake.  The  shell  or  casing  is  so  constructed  that  it 
permits  an  equal  pressure  of  water  upon  both  sides  of 
the  disk — a  sufficient  quantity  of  the  water  being  al- 
lowed to  pass  through  the  machine  to  carry  off  the 
heat  due  to  the  energy  absorbed. 

An  ingenious  form  of  valve  operated  by  the  slight 
angular  motion  of  the  dynamometer 
varies  the  supply  of  water,  and  con- 
sequently the  pressure  between  the 
frictional  surfaces,  thus  securing  auto- 
matic regulation.  Referring  to  Figs. 
20  to  24,  A  (Fig.  20)  is  an  iron 
disk  keyed  to  the  crank-shaft  B. 
The  sides  of  this  disk  are  finished 
smooth,  and  each  side  has  one  or 
more  shallow  radial  grooves,  as  shown 
at  X  (Fig.  21).  The  outer  shell 
consists  of  two  pieces  of  cast-iron, 
C  C,  bolted  together,  but  held  at 
a  fixed  distance  apart  by  the  iron 
ring  D — whose  thickness  is  the  same  as  that  of  the 
disk  A — and  by  the  edges  of  the  copper  plates  E  E. 
Each  of  these  plates  at  its  inner  edge  makes  with  the 
cast-iron  shell  a  water-tight  joint  by  being  "  spun  "  out 
into  a  cavity  in  the  iron  and  held  by  driven  rings  F  F. 
Thus  between  each  copper  plate  and  its  cast-iron  shell 
there  is  a  water-tight  compartment,  WW,  into  which 
water  from  the  city  pipes  is  admitted  at  G,  and  passing 


5« 


£>  YNAMOME  TERS 


to  the  opposite  compartment  through  passages,  as 
shown  at  O,  is  discharged  through  a  small  outlet  at  H- 

The  chamber  MNN  is  filled  with  oil,  which  finds  its 
way  from  TV  to  M  along  the  grooves  in  the  disk  A. 

The  shaft  is  free  to  revolve  in  the  bearings  of  the 
cast-iron  shell  CC.  The  shell  has  an  arm  carrying 
weights,  as  shown  in  Fig.  21.  The  arm  has  its  angular 
motion  limited  by  stops  at  P  and  Q. 


FIG.  21. 


An  automatic  valve  at  V  (Fig.  22 — and  shown  in 
sections,  Figs.  23  and  24)  regulates  the  supply  of 
water  to  the  machine. 

The  valve  consists  of  two  brass  tubes  fitted  one  in- 
side the  other,  but  free  to  revolve  relatively  to  one 
another.  The  inside  tube  has  one  end  closed.  Each 
tube  has  slots  parallel,  or  nearly  parallel,  to  its  axis. 
One  tube  connects  with  the  supply-pipe  S,  the  other 
with  a  pipe  rigidly  fixed  to  the  brake  and  com- 
municating with  one  of  the  compartments  W.  A  flex- 


AND    THE  MEASUREMENT  OF  POWER. 


59 


ible  tube,  R,  encloses  the  whole.  The  valve  is  so 
adjusted  that  a  slight  angular  motion  of  the  brake 
varies  the  free  water  passage  through  the  slots  (see 
Fig.  23) ;  and  the  aperture  at  H,  through  which  the 
water  is  discharged,  being  small  and  constant,  the  press- 


ure of  the  water  in  the  chambers  W  W  is  thus  auto- 
matically varied. 

The  dynamometer  is  operated  as  follows :  The 
chamber  NNM  being  filled  with  oil,  weights  are  sus- 
pended from  the  arm  to  give  the  desired  load.  The 
engine  is  started,  and  when  up  to  speed  a  valve  is  suit- 
ably opened  in  the  water-pipe  leading  to  the  automatic 
valve  (V],  which  latter  being  open,  allows  water  to 
pass  to  the  compartments  W  W.  The  pressure  of  this 


60  D  YNAMOME  TERS 

water  forces  the  copper  plates  against  the  sides  of  the 
revolving  disk  A — with  which  they  were  already  in 
contact — causing  sufficient  friction  to  balance  the 
weights  upon  the  arm,  which  then  rises.  This  motion 
operates  the  automatic  valve,  checking  the  flow  of 
water  to  the  brake  and  regulating  the  moment  of  the 
friction  on  the  disk  to  the  moment  of  the  weights  ap- 
plied to  the  arm  of  the  brake.  The  first  trial  of  the 
machine  gave  remarkable  results,  the  arm  standing 
midway  between  the  stops,  with  only  a  slight  and  slow 
vibration,  and  this  without  the  use  of  a  dash-pot.  The 
water  seems  a  little  sluggish  in  its  action  in  response 
to  the  motion  of  the  regulating  valve,  so  that  there  is 
no  sudden  vibration  of  the  arm,  and  the  load  is 
practically  constant.* 

In  experimenting  with  a  5O-horse-power  Alden 
brake,  Prof.  Goss,  of  Purdue  University,  has  found 
that  the  operation  of  the  brake  is  very  materially 
improved  by  cutting  spiral  grooves  on  each  face  of 
the  revolving  plate  and  connecting  the  inner  com- 
partment between  the  copper  disks  with  two  pipes — 
the  one  near  the  hub,  and  the  other  at  the  outer  cir- 
cumference of  the  shell.  This  admits  of  a  better  dis- 
tribution and  circulation  of  the  oil,  which  is  fed  from 
the  pipe  connected  to  the  chamber  near  the  hub. 
From  this  chamber  the  oil  is  carried  to  the  circumfer- 
ence, both  by  the  radial  grooves  and  by  the  spiral 
groove  which  crosses  the  former,  thus  ensuring  a  very 
even  and  uniform  distribution  of  the  oil,  which  then 
passes  out  at  the  circumference  into  a  strainer  situated 

*  Trans.  A.  S.  M.  E.,  vol.  VI. 


AND    THE  MEASUREMENT  OF  POWER.  6 1 

above  the  oil  feed-pipe,  whence  it  is  again  carried  to  the 
central  chamber  at  the  hub,  and  the  process  repeated 
as  long  as  the  machine  is  in  operation. 

An  interesting  application  of  the  Alden  brake  has 
been  made  in  the  Experimental  Laboratory  of  Purdue 
University  by  which  the  power  of  an  eight-wheeled 
passenger  locomotive  is  absorbed.  In  this  arrange- 
ment, Fig.  25,*  the  locomotive,  weighing  43  tons,  is 
'  mounted  .with  its  drivers,  which  are  63  inches  in 
diameter,  upon  heavy  supporting  wheels,  of  the  same 
diameter,  free  to  revolve  by  contact  with  the  drivers 
in  either  direction  :  the  prolonged  axles  of  the  support- 
ing wheels  are  each  provided  with  a  large  flat  cast  iron 
disk  keyed  to  the  shaft,  which  is  allowed  to  rotate  in 
a  closed  case  between  plates  of  copper,  about  three- 
sixteenths  inch  thick,  which  can  be  forced  against  the 
rotating  disk  by  hydraulic  pressure  as  in  the  Alden 
dynamometer.  Each  brake  was  designed  for  a  load  of 
200  H.  P.  under  a  moment  of  10500  foot-pounds,  with 
a  maximum  water  pressure  of  40  pounds  per  square 
inch.  The  shaft  to  which  the  disk  is  keyed  is  7$  inches 
in  diameter.  The  disk  is  56  inches  in  diameter  and  2f 
inches  thick ;  it  is  provided  with  thirty-two  radial  oil- 
grooves  on  each  face,  besides  which  a  spiral  groove  of 
about  4  inches  pitch  is  cut  across  the  face  intersecting 
the  radial  grooves,  thus  thoroughly  distributing  and 
circulating  the  oil  as  in  the  smaller  brake  previously 
alluded  to.  The  locomotive  is  free  to  move  forward 
or  backward  only  through  a  very  small  distance  (about 
a  quarter  of  an  inch),  its  tendency  to  motion  in  either 

*  From  Am,  Machinist,  April  28,  1892. 


62 


DYNAMOMETERS 


AND    THE  MEASUREMENT  OF  POWER.  63 

direction  being  measured  by  a  system  of  levers  and 
weights  connected  to  the  draw-bar  by  which  the  trac- 
tion of  the  engine  can  readily  be  weighed.  Any  desired 
load  and  speed  can  be  maintained  by  means  of  the 
powerful  friction-brakes  which  are  bolted  securely  to 
stone  foundations — in  this  respect  differing  from  the 
Alden  dynamometer,  which  is  free  to  rotate  through  a 
small  arc.  The  smoke  is  exhausted  through  the  roof 
of  the  building  by  a  Sturtevant  blower  which  is  placed 
above  the  smoke-stack,  but  not  in  connection  with  it. 

An  absorption-dynamometer,  designed  by  Mr.  Wm. 
Froude*  to  measure  the  power  of  large  marine  engines 
is  essentially  another  form  of  water-brake. 

In  this  arrangement,  the  engine  in  delivering  its 
power  may  be  assumed  to  be  winding  up  a  weight  out 
of  indefinite  depth,  but  the  weight  instead  of  being 
constant  and  assigned  (as  in  the  case  of  the  suspended 
weight  on  a  friction-brake)  will  vary  with  the  speed  of 
rotation  much  in  the  same  way  as  the  resistance  of  the 
propeller  itself  does;  and  thus  the  work  performed  by 
the  engine  under  trial  will  more  closely  resemble  its 
natural  work,  though  the  same  circumstance  renders 
necessary  an  automatic  method  of  recording  the  varia- 
tions of  the  resistance  which  occurs  during  the  trial. 
The  reaction,  as  will  be  shown,  instead  of  arising  from 
the  friction  of  two  solid  surfaces,  will  consist  of  a  series 
of  fluid  jets  which  are  maintained  in  a  condition  of  in- 
tensified speed  by  a  sort  of  turbine  revolving  within  a 
casing  filled  with  water,  both  turbine  and  casing  being 
mounted  on  the  end  of  the  screw  shaft  in  place  of  the 


Proc.  Brit.  Inst.  M.  E.,  vol.  for  1877. 


64  D  YNA  MO  ME  TEKS 

screw ;  the  turbine  revolving  while  the  casing  is  dy- 
namometrically  held  stationary.  The  jets  are  alter- 
nately dashed  forward  from  projections  in  the  turbine 
against  counter-projections  in  the  interior  of  the  casing, 
tending  to  impress  forward  rotation  upon  the  casing, 
and  are  in  turn  dashed  back  from  the  projections  in 
the  casing  against  those  in  the  turbine,  tending  to  re- 
sist the  turbine's  rotation.  The  important  point  is 
that  the  speed  of  jets  is  intensified  by  the  reactions 
to  which  they  are  alternately  subjected ;  and  thus,  in 
virtue  of  this  circumstance,  a  total  reaction  of  very 
great  magnitude  is  maintained  within  a  casing  of  com- 
paratively very  limited  dimensions. 

The  nature  of  this  arrangement  will  be  understood 
by  referring  to  the  following  figures,  which  represent 
the  dynamometer  as  designed  to  measure  2000  H.  P. 

In  Fig.  26,  A  represents  the  screw  end  of  the  screw- 
shaft  ;  BB  shows  in  section  what  has  been  termed 
"  the  turbine  " ;  it  is  a  disk  or  circular  plate  5  feet  in 
diameter,  with  central  hub  keyed  to  the  shaft  in  place  of 
the  screw,  and  revolving  with  the  shaft.  The  disk  is 
not  flat  throughout  its  entire  zone,  being  shaped  into 
a  semi-oval  section  which  sweeps  around  the  whole 
circumference  concentric  with  the  axis.  In  Fig.  27 
Fig.  26  is  repeated  and  the  "casing"  is  added,  CC 
representing  the  front  and  DD  the  back. 

The  face  is  shaped  into  a  channel  the  counterpart  of 
that  in  the  turbine  disk,  so  that  the  two  semi-oval  chan- 
nels in  effect  form  one  complete  channel.  The  back  of  the 
casing  encloses  the  turbine  entirely,  but  without  touch- 
ing it.  The  casing  is  also  provided  with  a  hub,  which 
is  an  easy  fit  over  that  of  the  turbine,  so  that  the  latter 


AND    THE  MEASUREMENT  OF  POWER.  6$ 

is  free  to  revolve  within  the  casing,  which  is  stationary. 
Both  casing  and  turbine  are  provided  with  a  series  of 
twelve  fixed  diaphragms,  one  of  which  is  showgi  in  Fig. 
28.  These  diaphragms  cut  the  channel  obliquely,  being 
semicircular  in  outline,  so  that  when  set  at  an  angle, 
as  shown  in  side-view  (Fig.  29), their  circular  edges  fit  the 


FIG.  27. 


FIG. 


FIG.  29. 


PROUDE'S  M 


DYNAMOMETER. 


oval  bottom  of  the  channel,  while  their  diameters  span 
the  major  axis  of  the  oval.  Thus  is  formed  by  casing 
and  turbine,  when  the  diaphragms  are  opposite  to  each 
other,  a  series  of  cells ;  and  as  the  function  of  the  tur- 
bine is  to  rotate  while  the  casing  remains  at  rest,  one 
half  of  each  cell  is  moving  past  the  other  half  in  such 
a  manner  that  the  moving  half,  if  viewed  from  its  sta- 


66  D  YA'AMOME  TEK$ 

tionary  counterpart,  would  appear  to  be  advancing 
antagonistically  towards  it.  The  effectiveness  of  this 
combination  to  resist  rotation  will  be  seen  to  depend 
essentially  on  this  assumed  antagonistic  motion.  The 
channel  and  casing  is  filled  with  water,  and  the 
turbine  is  made  to  rotate  as  described.  When  the  tur- 
bine is  thus  put  in  motion,  the  water  contained  in  its 
half-cells  is  urged  outward  by  centrifugal  force,  and  in 
obeying  this  impulse  it  forces  inward  the  water  con- 
tained in  the  half-cells  of  the  stationary  casing,  and 
thus  a  continuous  current  is  established — outward  in 
the  turbine's  half-cells,  and  inward  in  those  of  the  casing. 

The  current,  though  in  fact  originated  solely  by  cen- 
trifugal force,  possesses,  when  once  called  into  exist- 
ence, a  vitality  and  power  of  growth  quite  independent 
of  centrifugal  force  and  dependent  on,  what  has  been 
called,  the  virtually  antagonistic  attitude  or  motion  of 
the  two  sets  of  diaphragms  and  the  cells  of  which  they 
are  the  boundaries.* 

It  can  be  shown  that,  with  a  dynamometer  of  given 
dimensions,  the  reactions  which  tend  to  stop  rotation 
of  the  turbine  and  to  give  rotation  to  the  casing  will  be 
as  the  square  of  the  speed  of  rotation  of  the  shaft  to 
which  it  is  attached;  and  that  by  comparing  two 
similar,  but  differently-dimensioned  turbines,  their  re- 
spective moments  of  reaction  for  the  same  speed  of  ro- 
tation should  be  as  the  fifth  powers  of  their  respective 
diameters. 

Mr.  Froude  constructed  an  experimental  pair  of  dy- 
namometers in  which  the  turbine  diameters  were  re- 

*  For  discussion  of  principles  involved,  see  Appendix  in  vol.  for 
1877  Proc.  Brit.  Inst.  M.  E. 


AND    THE  MEASUREMENT  OF  POWER. 


spectively  12  inches  and  9.1  inches. 


/I2V 

Now(-;)   =4. 

and  therefore  the  ratio  of  moments  of  the  two  instru- 

The 
,  but 


ments  at  a  given  speed  should  also  have  been  4. 
ratio  determined  by  experiment  was  in  fact  3.8 
the  small  difference  is  referable  to  the  circumstance 


FIG.  31.— FROUDE'S  MARINE-ENGINE  DYNAMOMETER. 

that  in  the  larger  of  the  two  instruments  the  internal 
surface  was  rougher  and  the  friction  of  the  water 
greater.  The  data  thus  obtained  not  only  verify  the 
scale  of  comparison  based  on  the  fifth  power  of  the  re- 
spective diameters,  but  also  furnish  a  starting-point  by 
which  to  proportion  the  dimensions  of  an  instrument 
required  to  deal  with  any  given  horse-power  delivered 
at  a  given  speed. 

It  thus  appears  that  an  instrument  similar  to  that 
shown  in  Figs.  30  and  31  will  measure  2000  H.  P.  at  90 
revolutions  per  minute;  the  turbine  being  5  feet  in  di- 


68  D  \ 'NAMOME  TERS 

amcter,  and  formed  with  two  faces,  with  a  double-sided 
casing  to  match.  This  double  arrangement,  it  may  be 
added,  while  it  supplies  a  double  circumferential  reac- 
tion with  a  given  diameter,  has  the  advantage  of  oblit- 
erating all  mutual  thrust  on  working  parts.  In  order 
to  adapt  this  dynamometer  to  measure  varying  horse- 
powers— that  is,  to  produce  readily  a  greater  or  less 
reaction  with  a  given  number  of  revolutions — two 
sliding  shutters,  E  E,  of  thin  metal,  fitted  between  the 
turbine  and  casing,  are  arranged  so  that  each  shutter 
may  be  carried  forward  by  a  screw-motion  governed 
from  the  outside. 

By  this  means  the  internal  water-ways  or  passages 
through  the  cells  are  contracted  and  the  reactions 
greatly  reduced. 

The  experiments  with  the  models  showed  that,  with 
any  given  speed  of  turbine,  the  reaction  could  be  re- 
duced with  a  perfectly  graduated  progression  in  any 
required  ratio  down  to  one-fourteenth. 

The  intensity  of  reaction  is  thus  easily  brought  un- 
der the  control  of  the  operator  within  a  wide  range. 
The  brake  represented  in  the  figures,  and  designed,  as 
stated,  for  an  engine  of  2000  H.  P.  at  90  revolutions 
per  minute,  is  also  capable  of  dealing  with  one  of  340 
H.  P.  making  120  revolutions  per  minute. 

The  mechanical  reaction  due  to  friction  in  the 
working  parts  of  the  instrument,  while  of  relatively 
small  amount,  is  in  effect  wholly  incorporated  with  the 
hydrodynamical  reaction,  and  is  thus  taken  account  of. 

In  applying  this  dynamometer  to  measure  the  power 
of  a  ship's  engines  the  instrument  is  mounted  upon 
the  screw  shaft  in  place  of  the  screw,  as  shown  in  Fig.  32. 


AND    THE  MEASUREMENT  OF  POWER. 


The  casing  is  provided  with  proper  apertures,  capa- 
ble of  being  closed  at  will,  to  permit  the  egress  of  air 
and  ingress  of  water. 

If  the  moment  to  be  measured  and  recorded  be  re- 
garded as  the  product  of  two  factors,  force  and  lever- 
age, of  which  the  one  varies  inversely  as  the  other,  it 
is  plainly  a  question  to  be  settled  by  considerations  of 


FIG.  32.— MARINE-ENGINE  DYNAMOMETER.    MODE  OF  APPLICATION. 

convenience,  whether  the  record  shall  involve  a  large 
force  delivered  at  short  leverage,  or  vice  versa.  In 
the  present  case  it  will  be  seen  that  a  large  leverage 
is  desirable  ;  for,  if  we  assume  the  force  to  be  acting  at 
the  circumference  of  the  casing,  say  3  feet  from  centre 

2OOO  ^X*   ^  3  OOO 

of  shaft,  there  will  be  required  ^^ .i4X3X9Q  =  389°4 
Ibs. — a  force  which  will  bear  large  reduction.  In  the 
arrangement  shown  (Fig.  32)  the  leverage  has  been  in- 
creased in  the  ratio  of  10  to  I. 

The  lever  here  shown  consists  of  a  rod  F  and  wire 
rope  £,  connected  to  the  casing  C  at  one  end  and  unit- 


70  D  YNA  MO  ME  TERS 

ing  in  H  at  the  other.  As  the  force  at  H  acts  down- 
wards, it  will  be  seen  that  F  is  in  compression  and  G 
in  tension. 

A  suitable  weighing  apparatus,  consisting  of  a  sys- 
tem of  flat  springs  and  levers,  is  provided  for  ascertain- 
ing the  load,  to  which  is  attached  a  recording  device 
connected  to  the  screw-shaft  through  the  rod  L,  which 
takes  its  motion  by  bevel  gears  directly  from  the  shaft. 

More  recently,  Prof.  Osborne  Reynolds,*  of  Owens 
College,  Manchester,  has  constructed  several  of  these 
water-brakes  for  experimental  purposes  ;  and  as  the 
^result  of  his  experience  he  finds  that  air  is  drawn  from 
'the  water  and  accumulates  in  the  centre  of  the  cells, 
-^occupying  water  space  and  diminishing  resistance, 
besides  producing  an  irregular  motion.  This  would  be 
prevented  if  passages  could  be  provided  through  the 
outside  to  the  axis  of  vortex  within,  carrying  a  supply 
of  water  at  or  above  atmospheric  pressure,  so  as  to  pre- 
vent the  pressure  at  this  point  falling  below  that  of  the 
atmosrJliere.  This  was  accomplished  by  Prof.  Reynolds 
by  perforating  the  vanes  of  the  turbine  and  supplying 
water  through  the  perforations.  It  also  appeared  that 
by  having  similar  perforations  in  the  casing  open  to  the 
atmosphere  the  pressure  at  centre  of  vortex  could  be 
rendered  constant,  whatever  the  supply  of  water  and 
speed  of  wheel,  so  that  it  would  then  be  possible  to 
run  the  brake  partially  full  and  regular;  resistance  from 
nothing  to  maximum,  without  sluices. 

These  conclusions  being  verified  on  a  small  model 
(4-inch  turbine),  three  larger  brakes  with  i8-inch  wheels 

*  See  Proc.  Brit.  Inst.  C.  E-,  vol.  xcix,  also  Van  Nostrand's 
Science  Series,  No.  99. 


AND    THE  MEASUREMENT  OF  POWER.  71 

were  constructed.  These  brakes  proved  everything 
desirable  except  when  running  under  a  constant  load 
with  varying  speeds.  This  matter  was  considered  dur- 
ing their  construction,  and  an  arrangement  was  devised 
by  which  the  supply  and  exit  of  water  to  and  from  the 
brake  was  automatically  controlled  ;  the  lifting  of  the 
lever  opening  the  exit  and  closing  the  supply  so  as  to 
diminish  the  quantity  of  water  in  the  brake,  and  vice 
versa. 

During  the  twelve  months  these  brakes  have  been 
in  use  they  have  received  no  attention  whatever. 
The  casing  is  provided  with  a  lever  4  feet  long  from 
centre  of  shaft  to  the  weight.  When  the  speed  of 
engines  reaches  about  20  revolutions  per  minute  the 
levers  rise  (whatever  load  they  have  on),  and  though 
always  in  slight  motion,  they  do  not  vary  half  an  inch 
until  the  engines  stop  ;  during  the  run,  the  load  on  the 
brakes  may  be  altered  at  will  without  any  other  adjust- 
ment. 

The  engines  to  which  the  brakes  were  connected 
were  each  designed  to  work  with  any  steam-pressure 
up  to  200  pounds  per  square  inch,  at  any  piston-speed 
up  to  1000  feet  per  minute,  and  to  have  expansion-gear 
to  cut  off  from  o  up  to  two-thirds  stroke. 

Each  engine  was  furnished  with  a  fly-wheel  weigh- 
ing 1 200  pounds. 

The  dimensions  of  engines  were  as  follows : 
High-pressure  . .      5  inches  diameter,  10  inches  stroke 
Intermediate...     8       "  "  10       "  " 

Low-pressure...    12       "  "  15       "  " 

All  the  cylinders  were  steam-jacketed,  but  arranged 
so  that  any  or  all  of  the  jackets  could  be  cut  out. 


72  D  YNAMOME  TERS 


CHAPTER   IV. 

TRANSMITTING-DYNAMOMETERS. 

Half  a  century  ago,  Morin  gave  as  the  requirements 
of  a  dynamometer  the  following,  viz.: 

First.  The  sensibility  of  the  instrument  should  be 
proportioned  to  the  intensity  of  efforts  to  be  measured, 
and  should  not  be  liable  to  alterations  by  use. 

Second.  The  indications  of  flexures  should  be  ob- 
tained by  methods  independent  of  the  attendance, 
fancies,  or  prepossessions  of  the  observer,  and  should 
consequently  be  furnished  by  the  instrument  itself,  by 
means  of  tracings,  or  material  results,  remaining  after 
the  experiments. 

Third.  We  should  be  able  to  ascertain  the  effort 
exerted  at  each  point  of  the  path  described  by  the 
point  of  application  of  the  effort,  or,  in  certain  cases, 
at  each  instant  in  the  period  of  observations. 

Fourth.  If  the  experiment  from  its  nature  must  be 
continued  a  long  time,  the  apparatus  should  be  such 
as  can  easily  determine  the  total  quantity  of  work  ex- 
pended by  the  motor. 

To  meet  these  conditions,  Morin  made  the  spring- 
dynamometer,  in  order  to  obtain  the  magnitude  of  a 
force,  as,  for  instance,  the  traction  of  a  horse  on  a 
loaded  wagon  or  canal-boat. 

In  this  dynamometer  a  force  was  measured  by  the 
flexure  produced  by  it  on  two  springs  connected  at 


AND    THE   MEASUREMENT  OF  POWER.  73 

their  ends  and  loaded  in  the  middle.  When  a  steel 
bar  of  rectangular  cross-section  is  placed  freely  upon 
two  supports,  and  subjected  in  the  middle  to  a  force  P 
perpendicular  to  its  length,  its  flexure,  s,  so  long  as  it 
does  not  exceed  the  limits  of  elasticity,  will  be  : 

First.  Proportional  to  the  effort  P. 

Second.  Proportional  to  the  cube  of  the  arm  of  the 
lever  /  of  this  effort. 

Third.  In  an  inverse  ratio  of  the  width  of  the  bar 
b,  in  a  direction  perpendicular  to  the  plane  of  flexure. 

Fourth.  In  an  inverse  ratio  of  the  cube  of  the  thick- 
ness of  the  bar  /i,  at  its  middle  point. 

Fifth.  In  an  inverse  ratio  of  the  modulus  of  elas- 
ticity, E,  for  the  material  of  the  bar. 

The  deflection  for  the  force  P  will  be,  therefore, 

PI*          i 
s  =  -  X  -g  =  equation  of  elastic  curve, 

or,  since  W  =  ---  =  moment  of  flexure  for  rectan- 
gular strip,  we  have  for  deflection 

i  pr 


Since  we  have  to  take  into  account  the  deflection  of 
two  springs, 

=  1  ^_ 
~  2  Eb/f 

Now,  if  the  longitudinal  profile  of  the  bar  is  para- 
bolic, the  flexure  will  be  double  that  of  a  spring  of 


74  •#  YNA  MOMETERS 

uniform    thickness,    while    the    strength    remains   the 
same.     Hence  we  have 


where  n  is  a  number  to  be  determined  by  experiment. 

If  in  the  construction  of  a  spring-dynamometer, 
known  weights  be  applied,  and  the  deflection  s  ob- 
served, the  number;/  can  be  calculated  and  used  in  the 
construction  of  a  scale.  Morin  found  that  with  good 
steel  the  deflection  may  reach  one  tenth  of  the  length 
of  the  spring  before  the  relation  between  it  and  the 
force  changes. 

In  order  to  meet  the  second,  third,  and  fourth 
requirements  above  mentioned,  a  self-registering 
apparatus  was  used,  by  which  the  work  performed  was 
traced  upon  a  continuous  roll  of  paper,  set  in  motion 
by  suitable  wheel-work.  When  required  to  determine 
the  force  of  rotation  of  a  shaft  or  pulley  the  above 
dynamometer  requires  modification ;  the  essential 
features,  however,  remain  the  same. 

The  following  description  illustrates  the  application 
of  the  foregoing  principles  to  the  rotation-dynamom- 
eter. 

Upon  a  shaft  resting  on  two  cast-iron  supports  are 
three  pulleys  of  the  same  diameter,  Figs.  33  and  34. 
A  is  fixed,  C  is  loose,  and  B  is  movable  around  the 
shaft  between  the  limits  which  we  shall  indicate.  This 
apparatus  being  placed  between  the  driving-shaft  and 
a  machine  whose  resistance  is  to  be  measured,  the  loose 
pulley  C  receives  the  power  from  the  driving-shaft  by 


AND    THE  MEASUREMENT*  OF  POWER. 


75 


means  of  a  belt,  which,  when   transferred  to  A,  sets 
the  shaft  5  in  motion. 

The  pulle'y  B  is  free  on  the  shaft,  and  is  connected 
to  it  by  means  of  two  parabolic  springs  which  are 
fastened  to  the  shaft,  and  at  the  end  G  to  the  rim  of  B. 
These  springs  turning  with  the  shaft  deflect  more  or 
less,  according  to  the  resistance  encountered,  and  when 
the  resistance  to  flexure  overcomes  the  resistance  of 

FIG.  ,3.  FIG.  34. 


LMJ 


MORIN'S  TRANSMI 


M-DYNAMOMETER. 


the  machine,  motion  is  transmitted  through  the  springs 
to  B. 

Upon  the  shaft  is  a  worm,  K,  having  a  stop,/,  so  that 
by  means  of  a  sliding  bar,  mn,  it  may  be  prevented 
from  revolving  with  the  shaft  during  the  experiment. 
By  a  suitably  arranged  train  of  gearing  a  series  of 
drums  is  set  in  motion,  by  means  of  which  a  roll  of 
paper  is  caused  to  pass  under  a  pencil,  P,  attached  to 
one  of  the  arms  of  pulley  B,  thus  recording  the  resist- 
ances, and  giving  a  measure  of  the  work  performed. 

Using  the  same  notation  previously  given,  and  sub- 


76  D  YNA  MCME  TERS 

stituting  R — radius  of  path  in  feet — for  L,  we  have  the 
work  done 

W=  27tRNP; 

where  P=  resistance  overcome  in  the  machine  driven 
by  the  dynamometer.  P  can  be  readily  ascertained 
when  deflection  of  spring  is  known.  One  of  the  prin- 
cipal objections  to  the  use  of  this  instrument  is  that 
the  centrifugal  force  of  the  rotating  pieces  enters  as  a 
factor  into  the  final  result  ;  for  accurate  work  this  will 
necessitate  corrections  for  different  speeds,  and  in  this 
respect  Morin's  dynamometer  does  not  fulfil  his  third 
requirement  of  a  good  instrument,  viz.:  "  We  should 
be  able  to  ascertain  the  effort  exerted  at  each  point  of 
the  path  described  by  the  point  of  application  of  the 
effort,  or,  in  certain  cases,  at  each  instant  in  the  period 
of  observations." 

Another  form  of  transmitting-dynamometer,  some- 
times called  the  differential  dynamometer,  was  intro- 
duced into  this  country  by  Mr.  Samuel  Batchelder,  of 
Saco,  Maine,  in  1836.  The  principle  of  this  machine 
is,  that  to  hold  a  weight  by  the  radius  of  a  circle  in  a 
horizontal  position  takes  as  much  power  as  to  lift  the 
same  weight  through  the  distance  which  would  be 
traversed  by  it  in  any  given  number  of  revolutions  if 
rotated  in  the  circle  and  in  the  time  required  for  such 
number  of  revolutions.  We  have  already  seen  that  this 
is  the  governing  principle  of  the  Prony  brake  where  the 
lever  is  maintained  in  a  horizontal  position,  the  work 
being  estimated  as  though  the  weight  suspended  at  the 
end  of  the  lever  rotated  in  a  circle  whose  radius  was 
equal  to  the  length  of  arm  L.  Though  alike  in  princi- 
ple, the  methods  by  which  these  two  dynamometers 


AND    THE  MEASUREMENT  OF  POWER.  JJ 

operate    are    radically   different.     The    Batchelder    in- 
strument, improved  and  modified,  is  now  made  by  the 


FIG.  35.-WEBBER    B 


Lawrence  Machine  Co.,  and  known  as  the  Webber  bal- 
ance-dynamometer. 

The  following  description  of  this  machine  (see  Fig. 


78  DYNAMOMETERS 

35)  is  taken  from  a  paper  by  S.  S.  and  W.  O.  Webber, 
read  before  the  Society  of  Mechanical  Engineers.* 

"  On  the  receiving-shaft  are  fixed  a  pair  of  fast- 
and-loose  pulleys  at  one  end,  and  a  spur-gear  at  the 
other.  This  spur-gear  drives  a  corresponding  gear  of 
the  same  size  and  number  of  teeth,  which  is  fixed  on 
the  end  of  a  sleeve  or  collar,  having  on  its  other  end  a 
bevel-gear  which  forms  one  side  of  what  is  known  as  a 
'  box'  or  'compound  '  gear.  A  corresponding  gear  on 
the  opposite  side  of  the  '  box '  is  fixed  on  the  delivering- 
shaft  which  passes  through  the  sleeve  above  mentioned, 
and  also  through  the  fulcrum  of  the  scale-beam.  The 
two  remaining  sides  of  the  box  are  composed  of  a  pair 
of  equal  and  similar  gears,  which  revolve  freely  around 
the  scale-beam  on  either  side  of  the  fulcrum.  "  One 
would  really  be  sufficient  for  the  purpose,  but  a  pair 
is  used  in  order  to  preserve  a  balance.  When  motion 
is  given  to  the  shafts  by  means  of  a  belt  to  the 
receiving-pulley,  the  intermediate  gears  revolve  about 
the  scale-beam  without  effect ;  but  when  a  belt  is  car- 
ried from  the  delivering-pulley  to  the  machine  to  be 
tested,  the  resistance  causes  the  intermediates  to  act 
with  the  effect  of  levers  on  the  scale-beam,  and  would 
put  the  latter  in  revolution  about  its  axis  or  fulcrum  if 
it  were  not  restrained  by  the  weights,  which  are  to  be 
added,  and  adjusted  until  a  balance  has  been  obtained. 
It  will  be  readily  seen  that  the  real  motion  of  the 
scale-beam,  were  it  free  to  move,  would  only  be  one 
half  that  of  the  shafts,  and  the  weights  in  actual  use 
are  therefore  double  their  apparent  value — or  .in  other 

*  Trans.  A.  S.  M.  E.,  vol.  iv. 


AA'D    THE  MEASURED  EXT  OF  POWER.  79 

words,  the  weight  marked  1000  pounds  is  in  reality  two 
pounds  instead  of  one." 

The  circumference  of  the  circle  through  which  the 
weight  would  travel,  were  it  free  to  move,  is  ten  feet, 
therefore  we  can  readily  calculate  the  horse-power  from 
the  following  : 

HP  -     Pv      -   p 

~  33  ooo  ~~       33  ooo 

since  2nR  =  10,  we  have 


33000' 

in  which,  as  in  our  former  notation,  P  —  pounds  weight, 
N  =  revolutions  "per  minute,  and  v  =  velocity  in  feet 
per  minute. 

The  weights  are  marked  for  N  =  100. 

Another  form  is  that  known  as  the  belt  transmission- 
dynamometer,  used  by  Dr.  Hopkinson  in  his  tests 
with  the  Siemens  dynamo-electric  machines. 

The  principle  involved  is  the  weighing  of  the  result- 
ing stress  from  a  deflected  belt,  and  by  this  means  as- 
certaining the  direct  stress  upon  the  belt  itself. 

As  previously  intimated,  the  power  exerted  by  a  belt 
is  the  difference  of  strain  on  the  two  sides  of  the  belt, 
multiplied  by  the  velocity  of  a  point  on  the  belt.  A 
belt  connecting  two  shafts,  when  at  rest,  has  the  same 
tension  in  all  its  parts,  but  as  soon  as  work  is  performed 
by  the  belt  this  uniform  tension  ceases,  the  driving- 
shaft  exerts  a  pull  on  the  driven  proportional  to  the 
resistance  overcome,  and  as  the  adhesion  of  the  belt  is 


8o  D  YNA  MOME  TERS 

brought  into  play,  one  side — that  on  which  the  pull  is 
exerted — is  tightened,  while  the  other  is  correspond- 
ingly slackened.* 

To  obtain  a  measure  of  this  difference  in  belt-strain, 
the  dynamometer  shown  in  Fig.  36  was  designed  by 
Mr.  Robert  Briggs. 


FIG.  36. — BRIGGS  BELT-DYNAMOMETER. 

In  this  arrangement  it  is  evident  that  when  at  rest,  or 
running  with  no  resistance,  the  system  will  come  into 
equilibrium  with  equal  but  opposite  angles  for  both  the 
lower  and  upper  belt— provided  the  weight  of  the  car- 
rier-pulleys, the  frame  supporting  same,  and  the  weight 

*  In  a  series  of  experiments  on  leather  belting  made  by  Wm. 
Sellers  &  Co.  in  1885  it  was  shown  that  the  sum  of  the  belt-tensions 
is  not  constant,  but  increases  with  the  load.  This  is  contrary  to  the 
generally  accepted  theory  that  the  sum  is  constant,  but  subsequent 
experiments  have  shown  that  the  total  tension  actually  increases  as 
the  difference  increases,  whether  the  belt  be  horizontal  or  vertical. 


\ND    THE  MEASUREMENT  OF  POWER. 


Si 


of  the  belt  are  balanced.  It  can  be  shown  that  the 
resultant  of  strain  from  the  deflected  belt  varies  as  the 
cosine  of  the  angle  which  the  belt  makes  with  the  ver- 


FIG.  37. 

tical,  or  W=  2P  cos  a,  (Fig.  37) ;  therefore,  if  we  make 
the  angle  75°  31',  the  cosine  will  equal  0.250,  or 

cos-1  £=75°  31'. 

Let  cos  a  —  .25  ;  tension  on  tight  side  of  belt  =  7",  ; 
tension  on  slack  side  of  belt  =  T^ ;  weight  =  W '•  force 
transmitted  =  P\  then  will  71,  —  T,  =  P.  Now,  since 
W=  2P  cos  a,  and  cos  a  =  0.25,  we  have  W  —  2P  X  ±, 
hence 


If,  therefore,  a  weight  w  be  applied  on  the  scale- 
beam  so  that  it  exerts  a  force  W,  acting  downwards, 
there  will  be  transmitted  by  the  belt  a  force  P=  2 W, 
in  order  to  maintain  the  system  in  its  central  position; 
and  this  force  is  a  measure  of  the  driving  power  of  the 
belt! 


82 


D  Y A' A  MO  ME  7ERS 


Accepting  these  relations  of  angles  and  force,  the 
following  diagram,  Fig.  38,  will  show  the  relative  posi- 
tions of  the  arrangement  employed.  An  allowance  of 
y1^  inch  has  been  made  for  half  the  thickness  of  belt 
when  the  radii  of  the  line  of  the  belt  on  the  two  pulleys 
become  as  shown,  8.1  and  12.1  for  the  16-  and  24-inch 
pulleys  respectively. 


Diam.  <if  1'ulley  24'' 


J)iam.  oj  1'iMey  16 


FIG.  38. 


A  modification  of  this  dynamometer  was  designed 
by  Prof.  Elihu  Thomson,  in  which  the  angle  a  was 
made  equal  to  60°. 

Another  form,  in  which  the  difference  in  tension  of 
the  slack  and  driving  sides  of  the  belt  is  exerted  to 
vibrate  a  system  of  lever-arms  and  scale-beam,  is  that 
designed  by  Mr.  W.  P.  Tatham  of  Philadelphia,  and 
constructed  for  the  use  of  the  Franklin  Institute.* 

This  machine,  Fig.  39,  consists  of  a  double  gallows- 
frame  constructed  of  wood,  framed  together  at  the 
foot,  and  sustaining  at  the  top  a  cross-block,  from 
which  the  scale-beam  is  suspended.  This  beam  is 
capable  of  weighing  300  Ibs.,  and  is  graduated  to  25 
Ibs.  by  pounds  and  tenths. 

When  the  indicator  is  employed,  a  spring-balance  is 

*  See  Journal  Franklin  Institute,  Dec.  1882. 


AND    THE  MEASUREMENT  OF  POWER.  83 


FIG.  39. — TATHAM  DVNAMOMETKR. 


84  D  YNAMOME  TERS 

attached  near  the  extreme  end  of  the  beam  so  as  to 
exhibit  25  Ibs.  by  pounds  and  tenths. 

On  each  side  of  the  principal  centre  of  the  beam  and 
1.9  inches  therefrom  (unseen  in  the  figure)  are  knife- 
edges,  from  which  hang  two  links  suspending  the  free- 
moving  ends  of  two  cast-iron  lever-frames,  whose  ful- 
crums  are  outside  knife-edges  which  rest  upon  two 
iron  plates  bolted  to  the  gallows-frames. 

Each  of  these  lever-frames  carries  a  pulley  whose 
face  is  7  inches  and  whose  average  radius  is  4.30 
inches. 

The  axis  of  the  pulley  is  placed  8.78  inches  from  the 
link  knife-edge  and  4.39  inches  from  a  line  joining  the 
fulcrum  knife-edges.  The  effective  radius  of  the  pulley 
is  found  by  experiment  to  be  4.38  inches. 

The  middle  pulley,  partially  obscured  by  the  counter 
and  indicator-card,  represents  the  machine  on  trial. 

Its  shaft  is  produced  towards  the  observer,  and  by 
means  of  a  clutch  and  sleeve  carrying  a  small  spur- 
wheel  and  worm-screw,  the  counter  and  card  are  put 
in  or  out  of  gear  at  pleasure.  The  shaft,  produced 
towards  the  rear,  carries  an  outside  pulley  and  may  be 
coupled  directly  to  the  machine  on  trial,  or  connected 
with  it  by  a  belt. 

The  middle  pulley  has  a  face  of  7  inches  and  an 
average  circumference  of  38.594  inches.  Careful  meas- 
urements showed  that  the  actual  delivery  of  belt  per 
revolution  was  39.595  inches,  or  about  .005  inch  less 
than  the  3.3  feet  desired. 

The  larger  lower  pulley,  30  inches  diameter  and  7 
inches  face,  is  the  driver  on  the  first-motion  shaft.  It 
is  on  a  shaft  which  receives  power  from  an  outside 


AND    THE  MEASUREMENT  OF  POWER.  85 

source,  and  runs  in  journals  on  a  frame  adjusted  verti- 
cally in  slides  by  means  of  set-screws,  so  as  to  tighten 
the  belt. 

The  belt  runs  in  the  direction  of  the  arrows  on  the 
outside,  down  on  the  left  and  up  on  the  right.  But  in 
describing  its  operation,  it  is  best  to  follow  the  tension 
of  the  belt  in  a  direction  contrary  to  the  motion  of  the 
belt  itself. 

The  tension,  originating  at  the  lower  driving-wheel, 
acts  vertically  upon  the  left-hand  idler-pulley  at  the  ex- 
tremity of  its  effective  radius,  and  in  a  line  joining  the 
two  knife-edges  of  the  fulcrum,  and  therefore  the  effect 
of  this  part  of  the  belt  upon  the  scale-beam  is  nil. 

Losing  enough  force  to  overcome  the  friction  of  the 
idler-pulley,  the  remaining  tension  acts  vertically  :  first, 
by  reaction  upon  the  lever-frame  carrying  the  idler- 
pulley,  at  a  point  corresponding  to  the  extremity  of 
the  inside  effective  radius  of  the  pulley,  and  thence 
through  the  link,  upon  the  positive  side  of  the  scale- 
beam  ;  and  second,  upon  the  middle  pulley  representing 
the  machine  on  trial.  These  forces  are  equal  and  op- 
posite. 

The  tension  acting  upon  the  middle  pulley,  there 
performs  the  work  which  is  to  be  measured  and  is  re- 
duced thereby.  The  remainder  acts,  first,  by  reaction 
on  the  middle  pulley,  and,  second,  directly  upon  the 
lever-frame  carrying  the  right-hand  idler-pulley  as  be- 
fore, and  thence  through  the  link  to  the  negative  side 
of  the  scale-beam.  These  two  forces  are  equal  and 
opposite. 

The  tension  then  passes  over  the  idler  through  the 
fulcrum,  as  before,  to  the  place  of  beginning.  The 


86  D  YNAMOME  TERS 

outside  slack  tension  has  therefore  no  influence  on  the 
scale-beam. 

It  is  evident  from  this  description  that  the  only 
forces  bearing  upon  the  scale-beam  are  the  tension  of 
the  tight  belt  on  the  positive  side  of  the  beam,  and  the 
tension  of  the  slack  belt  on  the  negative  side.  The 
scale-beam  therefore  weighs  the  difference  between 
the  two. 

The  horse-power  absorbed  by  the  machine  being 
tested  may  be  found  from  the  general  formula 


-   =  H.P. 


33000 

P  in  this  case  equals  the  number  of  pounds  shown  on 
scale-beam,  v  =  velocity  of  belt  =  2nRN,  where  N 
is  the  number  of  revolutions  per  minute;  but,  as  pre- 
viously shown,  the  velocity  of  the  belt  is  3.3  feet  per 
revolution,  therefore  the  equation  for  this  particular 
machine  becomes 

H.P.  =,  -PN 


IOOOO 

The  principal  centre  of  the  scale-beam  is  lengthened 
towards  the  observer,  and  at  its  nearest  extremity 
carries  a  vertical  lever-arm  attached  to  a  horizontal 
link  connecting  it  with  a  long  vertical  index-lever 
which  carries  a  pencil  at  its  lower  end,  moving  hori- 
zontally as  the  end  of  the  beam  vibrates  vertically. 
This  pencil  marks  upon  a  ribbon  of  paper  caused  to 
move  vertically  between  two  revolving  rollers,  which 
are  driven  by  the  worm-screw  upon  the  prolongation 


AND    THE  MEASUREMENT  OF  POWER.     ,      87 

of  the  shaft  of  the  middle  pulley  before  mentioned. 
One  hundred  revolutions  of  this  worm  cause  one  revo- 
lution of  the  worm-wheel  upon  one  of  the  rollers. 

The  scale-beam  being  attached  to  a  spring-balance 
when  the  indicator  is  used,  the  ordinates  of  the  curve 
traced  by  the  pencil,  plus  the  weights  hanging  on  the 
scale-beam,  will  represent  the  force  employed,  while 
the  abscissas  will  represent  the  motion. 

The  Tatham  dynamometer,  which  measured  the 
power  consumed  by  the  dynamo-electrical  machines 
tested  by  a  committee  of  judges  in  June,  1885  (see 
report  in  supplement  to  the  Franklin  Institute  Journal, 
Nov.  1885),  is  capable  of  measuring  TOO  horse-power. 
The  largest  machine  then  measured  required  70  H.  P.; 
the  smallest,  0.23  H.  P.  This  machine,  Fig.  40,  occupies 
a  floor-space  of  about  6  by  4  feet,  and  is  7^  feet  high. 
Upon  the  cast-iron  bed-plate,  which  is  provided  with 
levelling-screws,  are  erected  the  two  main  frames,  bolted 
together  and  united  at  the  top  by  an  arch  from  which 
the  scale-beam  is  suspended.  A  movable  A-frame  in 
two  parts  is  hinged  to  the  bed-plate,  and  when  in 
position  holds  firmly  the  journal-boxes  of  the  outside 
bearing  of  the  two  middle  shafts. 

When  opened,  it  gives  liberty  to  change  the  outside 
pulleys,  or  the  belts  which  run  upon  them. 

This  dynamometer  is  upon  the  same  principle  as 
the  machine  represented  in  P^g.  39,  but  differs  from  it 
in  that  the  single  pulley  upon  the  first-motion  shaft  of 
the  latter  is  replaced  by  three  pulleys  in  the  present 
machine.  See  skeleton  diagram  Fig.  41. 

All  of  the  pulleys  are  cast-iron  plate-pulleys,  turned 
all  over  and  accurately  balanced.  They  are  12$  inches 


88 


D  YXA  MOM  E  TEK  S 


FIG.  40. — THE  TATHAM  DYNAMOMETER.    IMPROVED  FORM. 


AND    THE  MEASUREMENT  OF  POWER. 


89 


face,  and  are  upon  steel  shafts  2  inches  diameter,  run- 
ning in  brass  boxes  which  are  from  6  to  8  inches  in 
length. 

The  pulley  D  is  25   inches  diameter,  crowned  and 
placed    upon   the   first-motion    shaft,    which    receives 


power  from  an  outside  belt.  The  pulley  B,  25  inches 
diameter,  ground  perfectly  true  and  flat,  is  upon  a 
shaft  which  conveys  the  power  to  the  machine  to  be 
tested.  In  measuring  a  motor,  its  power  is  applied  to 
the  pulley  B. 

The  two  pulleys  5"  are  crowned,  21  inches  diameter, 
and  their  shafts  run  in  bearings  which  are  upon  vertical 
slides  regulated  by  screws.  The  vertical  movement  of 
these  pulleys  regulates  the  tension  of  the  belt.  The 
pulleys  W  and  W  are  21  inches  diameter,  slightly 
crowned,  and  their  shafts  run  in  bearings  upon  the  two 
lever-frames  LF  and  LFt  each  of  which  has  its  ful- 
crum in  a  pair  of  knife-edges  at  F  resting  upon  the 
main  frame.  The  inside  ends  of  the  lever-frames  are 
suspended  by  links  LC  and  LC  to  the  scale-beam  FP at 


90  D  YNAMOME  TERS 

equal  distances  on  either  side  of  the  principal  centre  of 
the  beam.  There  are  two  adjustments  to  each  of  these 
lever-frames,  (i)  Two  micrometer-screws  adjust  the 
position  of  the  centre  of  the  pulley,  so  that  the  line  of 
effect  of  a  belt  hung  on  it  on  the  outside  will  pass 
through  the  fulcrum,  and  no  addition  of  weight  to  the 
belt  will  affect  the  scale-beam  ;  which  is  experimentally 
proved.  (2)  The  position  of  the  knife-edge  suspended 
to  the  link  is  adjusted  so  that  the  scale-beam  weighs 
accurately  any  weight  suspended  by  a  piece  of  belt 
hung  over  the  inside  of  the  pulley. 

The  endless  belt  used  was  a  four-ply  gum  belt,  12 
inches  wide  and  0.26  inch  thick. 

If  the  belt  were  0.21  inch  thick,  its  delivery  would 
have  been  6.6  feet  per  revolution  of  the  pulley  B. 

It  will  be  seen  by  the  construction  that  the  pulley 
B  is  actuated  by  the  difference  of  the  tensions  of  the 
two  parts  of  the  belt  tangent  to  it,  and  that  the  scale- 
beam  weighs  the  same  difference  of  tensions  of  the 
same  parts  tangent  to  the  pulleys  Wand  W. 

The  scale-beam  was  graduated  in  600  divisions  of  ^ 
inch,  each  representing  a  half-pound  with  the  travelling 
poise  used.  On  this  poise  is  a  small  beam  graduated 
in  hundredths,  so  that  the  small  poise  upon  the  small 
beam  is  capable  of  weighing  yfa  of  a  pound  when  the 
machine  is  in  motion.  The  more  rapid  the  motion  the 
more  delicately  can  the  weighing  be  accomplished. 

In  testing  dynamo-electrical  machines,  the  resistance 
measured  being  very  uniform,  it  was  only  necessary 
that  the  belts  used  should  be  of  even  thickness  and 
free  from  lumpy  spiicings,  to  get  rid  altogether  of  the 


AND    THE  MEASUREMENT  OF  POWER.  9! 

tendency  to  dance  which  otherwise  afflicts  the  beams 
of  belt-dynamometers. 

The  fastest  speed  made  by  the  dynamometer  dur- 
ing the  tests  was  1700  revolutions  per  minute,  which 
gave  the  belt  a  speed  of  2\  miles  per  minute.  The 
fastest  speed  of  any  test  was  about  1400  revolutions 
(9240  feet  of  belt)  per  minute  continued  for  ten  con- 
secutive hours,  during  which  the  belt  ran  over  1000 
miles. 

The  centrifugal  force  tending  to  break  the  belt  at 
this  speed  is  about  1350  pounds  on  each  part,  but  this 
force  does  not  come  on  the  journals  or  pulleys ;  it  is 
confined  to  the  belt  itself,  and  stretches  it  until  it  be- 
comes slack.  The  slack  is  taken  up  by  screwing  down 
either  of  the  pulleys  S,  and  when  the  machine  slows  or 
stops  the  belt  is  tight. 

In  getting  the  "  friction  "  of  the  pulley  B,  after  a 
test,  the  machine  was  run  light  at  the  same  speed  that 
it  had  run  loaded  during  the  test ;  thus  comprehending 
in  similar  measure  all  sources  of  resistance  whether 
from  friction  proper,  bending  and  straightening  the 
belt,  or  air-currents.  The  force  required  to  bend  and 
straighten  the  belt  was  sensibly  affected  by  the  tem- 
perature of  the  air. 

Before  the  dynamo  tests  began  it  was  observed  that 
the  air-currents,  caused  by  the  rapid  movement  of  the 
belt,  interfered  with  the  functions  of  the  scale-beam, 
and  it  was  found  necessary  to  place  sheet-iron  roofs 
over  the  upper  pulleys.  The  lubrication  is  accom- 
plished by  an  automatic  feed. 

A  suitable  counter  is  provided  to  register  the  number 


Q2  D  YXAMOME  TERS 

of  revolutions,  which  latter  can  be  observed  to  within 
a  fraction  of  one  revolution. 

It  is  also  provided  with  apparatus  to  record  the 
power  measured.  This,  however,  was  not  used  during 
the  tests  referred  to,  as  direct  weighing  was  found  so 
convenient,  and  the  results  could  be  so  quickly  calcu- 
lated. At  the  end  of  the  scale-beam  is  a  vertical  rod 
attached  below  to  an  iron  cylinder  which  floats  in 
mercury  in  a  cylindrical  iron  pipe.  The  beam  being 
balanced,  any  force  tending  to  raise  it  lifts  the  cylinder 
out  of  the  mercury  proportionally.  This  motion, 
multiplied  by  levers,  is  communicated  to  a  pencil-point 
which  moves  vertically  |  of  an  inch  to  the  pound 
and  records  the  weight  upon  a  paper  band  moving 
horizontally  one  inch  for  every  100  revolutions  and 
recording  them.  This  automatic  registration  of  weight 
is  applied  only  to  the  fractions  of  weight  between  the 
even  fifty  pounds,  the  principal  part  of  the  weight 
being  hung  at  the  end  of  the  scale-beam  in  the  usual  way. 

By  confining  the  registration  to  this  small  excess,  it 
is  registered  on  the  large  scale  above  mentioned. 
The  method  of  calculating  the  H.  P.  is  similar  to  that 
used  in  the  smaller  machine;  the  formula  being 


IOOOO 

P  is  in  half-pounds  since,  the  delivery  of  belt  per 
revolution  of  B  is  6.6  feet.  This,  however,  supposes  a 
belt  y2^  of  an  inch  thick.  A  thicker  belt  requires  a 
correction  in  accurate  work. 

Not  the  least  interesting  portion  of  the  report  of  the 
committee  referred  to  is  that  relating  to  the  "  Calibra- 


AND    THE  MEASUREMENT  OF  POWER.  93 

tion  of  the  Dynamometer."  In  order  to  prove  whether 
or  not  the  dynamometer  measured  correctly  the  power 
transmitted  through  it,  it  was  used  in  the  determina- 
tion of  the  mechanical  equivalent  of  heat  on  a  large 
scale.  The  water-churn  used  was  a  cylinder,  3  feet 
diameter  and  3  feet  long,  holding  1223  pounds  of 
water.  In  the  continuous  method,  devised  by  Profes- 
sor Marks,  the  water  entered  the  churn  at  nearly 
uniform  temperature  and  left  it  at  nearly  uniform 
temperature,  about  15.5°  Centigrade  higher  than  it 
entered.  The  operation  continued  for  three  hours. 
The  first  half-hour  was  occupied  in  bringing  the  exit- 
water  to  uniform  temperature,  when  the  experiment 
proper  began  and  continued  for  two  hours  and  a  half, 
during  which  over  five  tons  of  water  passed  through 
the  churn  and  was  raised  about  15.5°  Centigrade  by 
the  continued  exertion  of  about  46  horse-power.* 
The  result  as  calculated  was : 

Mechanical  equivalent  for  i°  Centigrade 1391.05  foot-pounds. 

"  "  "    i°  Fahrenheit 772. Si     "  " 

Still  another  modification  of  the  belt  dynamometer 
— which  has  in  its  favor  simplicity — is  that  shown  in 
Fig.  42.  Instead  of  employing  a  scale-beam  with 
movable  weights,  the  force  is  measured  by  difference 
in  actual  weight  of  the  machine  when  at  rest  and  when 
in  motion — the  driving  side  of  the  belt  being  on  the 
lower  idle  pulley.  In  this  case  the  dynamometer  is 
placed  upon  an  ordinary  platform-scale,  and  the  base 
filled  with  iron  or  other  suitable  material  which  will 

*See  article  by  W.  P.  Tatham  in  Journal  of  the  Franklin  Insti- 
tute, Dec.  1885. 


94 


D  YNAMOME  TERS 


outweigh  the  pull  of  the  belt.  This  is  weighed  (after 
the  belt  is  put  on  ready  for  running),  and  when  work 
is  performed  the  resistance  of  the  driven  shaft  tends  to 
straighten  out  the  belt,  and  thus  to  lift  the  weight  in 


the   base,  so   that,  if   weighed    when    the    maximum 
resistance  is  reached,  the  difference  in  weight  will  equal 

w. 

As  before,  the  driving  force  is  equal  to  P  =  Tl  —  Tv 
the  difference  in  tension  between  the  tight  and  slack 
sides  of  the  belt. 

From  an  inspection  of  the  accompanying  diagram, 
Fig.  43,  it  will  be  seen  that  as  the  pulley  B  is  free  to 
move  up  and  down,  the  angle  ft  will  be  less  the  greater 
the  tension  in  7", ,  for  the  greater  the  tension  in  Tt  the 
less  (proportionally)  there  will  be  in  7", ,  and  in  conse- 


AND    THE  MEASUREMENT  OF  POWER.  95 

quence  the  weight  of  B  will  cause  the  slide  to  which  R 
is  attached  to  drop. 

As  the  tension  in  Tl  is  equal  to  the  weight  acting  at 


FIG.  43. 

A  divided  by  twice  the  cosine  of  the  angle  which  it 

makes  with  the  vertical,  or,  in  the  present  case,  with  — , 

2 

we  have 

W 


a 

2  COS- 

2 


If  —  equal  the  angle  which   7",  makes  with  the  verti- 
cal, we  have  in  like  manner 


2COS- 
2 


where  w  equals  the  weight  of  the  slide  and  is  constant. 
The  weight  W  acting  at  A  is  the  difference  in  weight 


90  D  YNAMOME  TERS 

of  the  machine  when  at  rest  and  when  work  is  per- 
formed. The  angles  a  and  ft  are  variable,  their 
magnitude  depending  upon  the  load  passing  through 
the  belts.  A  convenient  method  of  obtaining  these 
angles  is  by  the  use  of  a  jointed  gauge  free  to  open  to 
any  desired  angle.  This  gauge  consists  of  two  thin 
strips  of  metal  or  wood  hinged  at  one  end,  and  pro- 
vided with  a  clamp-screw  or  thumb-nut ;  by  placing 
the  gauge  parallel  to  the  edge  of  the  belt  the  angle  at, 
or  /?,  made  by  the  belt  can  readily  be  obtained  by 
adjusting  the  legs  of  the  gauge  to  correspond  to  the 
angle  of  the  belt ;  by  transferring  this  angle  to  paper 
its  magnitude  may  be  measured  by  means  of  a  pro- 
tractor. 

A  belt-dynamometer  designed  by  Messrs.  Geo.  Wales 
and  F.  M.  Leavitt  and  built  under  the  direction  of 
Prof.  Jas.  E.  Denton,  in  1883,  for  the  use  of  the  Chicago 
Railroad  Exhibit  Committee  appointed  to  test  dynamo- 
meters, is  shown  in  Fig.  44. 

This  apparatus  was  designed  to  make  an  autographic 
portable  dynamometer  on  the  belt-angle  principle, 
using  the  angle  of  the  belt  as  the  primary  element  of 
force  measured.  The  belt  could  be  drawn  to  any 
angle  by  a  wrench  applied  to  a  chain-winding  pulley  G, 
and  the  ratio  of  the  belt-angle  to  the  difference  of  ten- 
sion was  given  by  the  gauge  a;  that  is,  the  reading  of 
the  point  d  on  the  semicircular  scale  gave  a  constant 
which,  multiplied  into  the  height  of  the  pencil  on  the 
paper-drum  h  and  into  the  scale  of  the  spring  Z, — which 
was  variable  over  a  large  range  by  sliding  the  spring 
and  arm  N  along  the  levers  H  and  /,— gave  the  differ- 
ences of  tension.  • 


AND    THE  MEASUREMENT  OF  POWER. 


98  D  YXAMOME  TERS 

The  length  of  paper  revolved  in  a  given  time  gave 
the  space  moved  through  by  the  belt.  The  train  of 
differential  gearing  J/,  driving  the  paper-drum,  gave  a 
wide  range  of  speeds  to  the  drum.  The  instrument 
was  successfully  applied  to  the  measurement  of  power 
on  a  200  incandescent-light  dynamo ;  and  with  a  tight 
belt  7  inches  wide  which  did  not  violently  vibrate,  a 
very  perfect  trace,  under  varying  loads,  could  be  ob- 
tained on  the  paper  by  the  use  of  a  flexible  pencil  point. 

The  time  was  indicated  each  minute  by  perforating 
the  paper  by  an  electric  spark. 

The  disadvantage  in  using  this  apparatus  and,  in 
fact,  most  forms  of  belt-dynamometer,  is  the  tendency 
of  the  belt  to  produce  excessive  vibration,  thus  causing 
very  irregular  readings. 

For  small  machines  which  can  be  mounted  on  skids 
or  other  supports,  and  placed  on  a  pair  of  platform- 
scales,  the  driving  power  can  be  obtained  directly  from 
the  difference  in  weight  when  at  rest  and  when  per- 
forming work,  provided  the  driving  shaft  be  placed 
vertically  over  the  driven  shaft  of  the  machine  :  in  this 
case  a  dash-pot  connected  with  the  scale-beam  would 
be  an  advantage  in  obtaining  steadiness  of  readings. 

As  previously  shown  (page  56),  the  power  trans- 
mitted to  a  machine,  or  given  out  by  a  motor,  can  be 
determined  by  supporting  the  machine  upon  trun- 
nions and  measuring  its  torque,  or  turning  moment. 

In  the  Brackett  cradle-dynamometer  the  torque  is 
determined  by  suitably  mounting  the  machine  to  be 
tested  upon  a  swinging  platform  suspended  from  knife- 
edges  and  supplied  with  a  scale-beam  and  sliding 
weight;  the  tendency  of  the  driving  belt  to  rotate  the 


AND    THE  MEASUREMENT  OF  POWER. 


99 


machine  may  be  weighed  on  the  scale-beam,  and  will 
give  a  measure  of  the  power. 

This   dynamometer  in  its  modified  and    improved 


FIG.  45. 

form  as  manufactured  by  Queen  &  Co.,  of  Philadelphia, 
consists  essentially  of  a  strong  stiff  platform,  Fig.  45, 
furnished  with  two  rigid  uprights  in  each  of  which  is 
fixed  a  heavy  steel  knife-edge  from  which  the  platform 
is  suspended.  These  knife-edges  rest  upon  firm  sup- 


1 00  D  YNAMOME  TERS 

ports  bolted  to  the  floor  and  so  constructed  that  a 
slight  swinging  motion  is  allowed  to  the  platform  upon 
which  the  machine  to  be  tested  is  mounted. 

To  one  of  the  swinging  uprights,  near  the  knife-edge, 
is  fixed  a  graduated  horizontal  lever  which  carries  a 
sliding  weight.  Adjusting  screws  are  provided,  by 
means  of  which  the  axis  of  rotation  of  the  armature  of 
any  given  machine  may  be  made  to  coincide  with  the 
axis  of  oscillation  of  the  cradle,  viz.,  the  line  which 
passes  through  the  two  knife-edges.  In  this  way  ma- 
chines of  various  makes  and  sizes  can  readily  be  put  in 
position  and  their  data  determined.  Provision  is  made 
to  enable  the  experimenter  to  determine  when  this 
adjustment  is  secured  by  use  of  a  circular  plate  of 
metal  fixed  to  the  inner  end  of  each  of  the  knife-edges, 
so  that  its  centre  coincides  very  closely  with  the  axis 
of  oscillation  of  the  cradle  ;  when,  by  means  of  the  ad- 
justing screws,  the  armature-shaft  is  made  concentric 
with  the  circular  plates,  as  determined  by  means  of  a 
gauge,  the  machine  is  in  the  proper  position. 

Counterweights  are  also  provided  which  can  easily 
be  set  so  that  the  centre  of  gravity  of  the  system,  in- 
cluding the  machine  and  the  cradle  together  with  its 
attachments,  shall  nearly  coincide  with  the  axis  of 
oscillation,  as  is  done  in  the  common  balance. 

Suppose  the  dynamo-machine  placed  upon  the  cradle 
and  the  whole  adjusted  as  above,  and  that  we  wish  to 
determine  the  mechanical  energy  requisite  to  produce 
a  given  current.  The  machine  being  at  rest  with 
its  driving  belt  off,  the  cradle  is  brought  to  equilib- 
rium by  means  of  the  sliding  weight,  and  the  position 
of  the  latter  is  noted.  The  machine  is  then  belted 


AND    THE  MEASUREMENT  OF  POWER.         IOf 

and  driven  at  the  proper  speed,  the  circuit  being  closed 
to  produce  the  required  current.  In  consequence  of 
the  interaction  between  the  armature  and  the  field- 
magnets  equilibrium  will  be  destroyed,  and  the  sliding 
weight  must  be  moved  to  a  new  position  in  order  to 
restore  it.  This  done,  the  new  position  is  noted.  The 
difference  between  this  and  the  former  position  is  the 
length  of  the  effective  arm  of  the  couple  which  acts 
against  journal  friction  and  the  resistance  of  the  arma- 
ture to  motion,  due  to  the  interaction  between  itself 
and  the  field-magnets. 

If,  as  before,  we  represent  the  length  of  this  effec- 
tive arm  in  feet  by  L,  the  weight  of  sliding  balance  in 
pounds  by  P;  the  number  of  revolutions  per  minute 
by  JV,  then  the  mechanical  effect,  W,  in  foot-pounds 
per  minute  absorbed  by  the  dynamo  or  given  out  by 
the  motor  will  be 

W=  27tLNP, 

an  equation  similar  to  that  previously  found  in  the  dis- 
cussion on  friction-brakes.  It  must  be  noticed,  how- 
ever, that  here  the  length  of  arm  L  is  not  the  total 
horizontal  distance  from  centre  of  sliding  weight  to 
centre  of  shaft  (centre  of  suspension),  as  in  the  Prony 
and  band  brakes,  but  is  the  difference  of  lever-arms 
Ll  and  Z,  measured  when  the  machine  is  in  open  cir- 
cuit (£,)  and  when  the  circuit  is  closed  (/,,),  so  that 
L  =  L,  —  L,. 

It  is  obvious  that  the  cradle-dynamometer  can  be 
used  to  measure  the  work  absorbed  by  any  machine 
which  can  be  conveniently  mounted  on  the  swinging 
platform  ;  the  effective  lever-arm,  L,  being  obtained  by 


I O2  D  YNA  MOME  TERS 

subtracting  the  arm  Ll ,  obtained  by  running  the  ma- 
chine light,  from  Lt,  obtained  when  the  machine  is 
performing  useful  work. 

In  any  case  the  mechanical  horse-power  can  be 
obtained  by  dividing  Wby  33  OCX). 

Besides  the  energy  required  to  turn  the  armature 
journals  in  their  bearings  and  to  produce  the  current, 
some  is  necessarily  spent  in  producing  disturbance  in 
the  air  about  the  armature.  The  amount  may  be  deter- 
mined by  means  of  the  cradle-dynamometer  if  desired, 
and,  when  found,  if  it  be  added  to  that  determined  as 
above,  the  total  energy  expended  upon  the  machine 
will  be  known.  The  energy  expended  upon  the  air  is 
in  most  machines  very  small,  and  may  be  neglected 
without  serious  error. 

The  manner  of  using  the  cradle-dynamometer  to 
measure  the  energy  developed  by  the  dynamo-machine 
when  used  as  a  motor  will  immediately  be  obvious, 
since  no  new  principle  is  involved. 

A  cradle-dynamometer  designed  for  a  capacity  of 
from  £  to  33  horse-power  (250  to  25000  watts)  will 
weigh  about  1200  Ibs.,  and  occupies  a  floor-space  of  4 
by  6  feet. 

Since  its  first  introduction  by  Prof.  Brackett,  the 
cradle-dynamometer  has  been  largely  used  for  measur- 
ing the  power  of  dynamos  and  motors.  Experience 
has  shown  that  where  the  power  of  a  single  dynamo  is 
concerned  and  a  vertical  driving  belt  can  be  used, 
this  dynamometer  is  sufficiently  accurate  for  all  prac- 
tical purposes,  the  variations  of  successive  measure- 
ments being  easily  kept  within  a  twentieth  of  a  horse- 
power, We  know  of  no  successful  attempt,  however, 


AND    THE  MEASUREMENT  OF  POWER.         1 03 

to  use  a  belt  in  any  other  direction,  the  difficulties 
being  that  the  knife-edges  are  liable  to  slip  sideways 
on  their  supports,  and  that  the  pull  of  the  belt  causes 
a  deflection  of  the  whole  apparatus,  which  interferes 
with  the  adjustments.  In  fact,  the  machine  should  be 
driven  from  beneath  and  not  from  above,  to  be  able  to 
make  the  latter  easily  and  satisfactorily. 

To  set  the  axis  of  the  machine  in  line  with  the 
knife-edges  a  special  device  is  used  in  the  Experimental 
Laboratory  of  the  Stevens  Institute,  and  is  regarded 
as  the  most  reliable  method  of  adjustment  in  use.  If 
an  error  is  made  of  one-thousandth  of  a  foot  sideways 
in  setting  the  machine  and  the  pull  of  the  belt  is,  say, 
500  pounds,  a  substitution  of  these  quantities,  with 
1000  revolutions  per  minute,  in  the  formula  shows 
that  an  error  of  one-tenth  of  a  horse-power  will  be 
caused  thereby.  The  device  mentioned — first  used  by 
Prof.  J.  E.  Denton  in  1883,  when  tests  were  made  for 
the  Chicago  Railway  Commission — consists  of  two 
equal  weights  hanging  from  each  end  of  a  piece  of 
belt  which  is  hung  over  the  pulley  of  the  machine. 
The  weights  together  should,  preferably,  be  about 
equal  to  the  pull  of  the  belt.  The  machine  is  adjusted 
so  that  hanging  these  weights  on  causes  no  change  in 
the  position  of  the  scale-beam,  and  any  irregularity  in 
the  pulley  is  eliminated  by  trying  it  with  the  pulley  in 
positions  180°  apart. 

The  next  apparatus  to  be  described  is  the  Floating 
Dynamometer,  the  invention  of  Prof.  J.  Burkitt  Webb 
of  Stevens  Institute. 

This  dynamometer,  Figs.  46  and  47,  consists  of  the 
approximately  square  tank  A,  containing  water  or  some 


104 


D  YNAMOME  7'ERS 


heavier  liquid,  as  brine.  In  this  is  floated  the  nearly 
square  caisson  C,  which  is  a  negative  tank,  i.e.,  one  having 
its  water-tight  surface  outside.  The  tank  rests  either 


FIG.  46.— WEBB'S  FLOATING  DYNAMOMETER— ELEVATION. 

on  the  floor  or  upon  skids,  B,  with  screws  for  adjusting 
the  tank  a  small  distance  sideways.  On  the  caisson  is 
mounted  any  suitable  machine  whose  plus  or  minus 
consumption  of  power  is  to  be  measured.  The  figure 
shows  four  gear-wheels  mounted  in  such  a  way  that 
their  running-friction  may  be  measured  in  an  exact 
manner.  The  power  absorbed  or  developed  by  other 
rotating  machines — as  steam-engines,  electric  motors, 
dynamos — may  thus  be  measured. 

The   caisson,    together   with  whatever   is    mounted 
upon  it,  is  termed  the  float,  and  the  weight  of  liquid 


AND    THE  MEASUREMENT  OF  POWER. 


105 


displaced  by  it  must  of  course  be  equal  to  its  own 
weight.  In  addition  to  this,  the  proportions  of  the 
caisson  must  be  such  as  to  bring  its  metacentre  very 
near  to  the  centre  of  gravity  of  the  float. 


effi 


FIG.  47.— WEBB'S  FLOATING  DYNAMOMETER— GROUND  PLAN. 

The  machine  to  be  tested  (i.e.,  the  combination 
of  gear-wheels  D,  or  other  machine)  is  driven,  by  a 
coupling,  E,  from  the  countershaft  F.  The  latter  sus- 
tains the  pull  and  vibrations  of  the  driving  belt  G 
and  transmits  to  the  machine  a  pure  moment  only. 
The  connecting  coupling  E  is  of  a  special  design,  and 


1 06  D  YNA  MOME  TERS 

has  the  property  of  acting  as  a  semi-rigid  universal 
joint.  As  a  universal  joint  it  allows  the  float  to 
deviate  from  its  normal  position,  when  forced  to  do  so, 
without  injury  to  the  apparatus,  while  its  rigidity  acts 
automatically  to  keep  the  machine-shaft  in  line  with 
the  countershaft. 

The  countershaft  is  furnished  with  a  speed-counter,  H, 
mounted  upon  a  lever,  which  can  be  operated  from  the 
front  of  the  dynamometer  to  throw  the  counter  in  and 
out  of  gear.  This  lever  is  furnished  with  a  special 
electric  lock,  which  holds  it  securely  in  or  out  of  gear, 
except  at  regular  intervals  when  the  electric  circuit  is 
broken  by  a  clock  and  the  lever  unlocked,  by  a  spring 
not  shown  in  the  figure.  The  period  of  time  during 
which  the  counter  is  operating  must  therefore  be  an 
integral  number  of  these  intervals;  in  default  of  some 
such  arrangement  for  securing  a  high  degree  of  preci- 
sion in  measuring  the  speed,  this  part  of  the  work  would 
be  considerably  less  precise  than  that  of  measuring 
the  moment.  The  electric-lock  may  be  incorporated 
in  the  construction  of  the  counter,  or  a  "  card  "  may- 
be run  from  the  countershaft  and  intervals  of  time 
marked  upon  it  automatically,  thus  recording  the  ex- 
act number  of  revolutions  during  each  interval. 

For  measuring  the  driving  moment  the  caisson  is 
furnished  with  two  adjustable  levels,  a  shaft-level,  /, 
and  a  moment-level,  J,  and  with  a  scale,  O,  and  sliding 
weight,  or  pee,  P.  The  shaft-level  is  set  so  as  to  show 
when  the  machine-shaft  is  level,  and  therefore  in  the 
same  horizontal  plane  as  the  horizontal  countershaft ; 
a  deviation  therefrom  being  corrected  by  varying  the 
quantity  of  water  in  the  tank.  This  adjustment  re- 


AND    THE  MEASUREMENT  OF  POWER.         IO? 

quires  no  great  accuracy.  The  moderately  sensitive 
moment-level,  y,  is  set  to  a  central  position  when  the 
coupling  is  disconnected  and  the  P  at  one  end  of  the 
scale,  then,  when  the  machine  is  running,  it  is  brought 
again  to  the  centre  by  shifting  the  P  until  the  caisson 
assumes  its  former  position.  The  product  of  the  num- 
ber of  pounds  of  the  /'multiplied  by  the  difference  in 
feet  between  its  two  positions  gives  the  driving  mo- 
ment, which,  when  multiplied,  as  usual,  by  6.2832 
times  the  number  of  turns  per  minute  and  divided  by 
33  ooo,  gives  the  horse-power.  Putting  L  for  the  num- 
ber of  feet  between  the  two  positions  of  the  P,  and  N 
for  the  number  of  revolutions  of  the  shaft  per  minute, 
we  have  as  before 

27tLNP 

Horse-power  =  —       — . 
33000 

It  is  customary  to  make  the  weight  of  P  such  that 
the  horse-power  per  hundred  or  per  thousand  revolu- 
tions can  be  read  directly  from  the  scale.  Thus  the 
scale  may  be  divided  into  feet  and  decimals  of  a  foot 
and  P  may  be  made  equal  to  33  -f-  2;r,  or  about  5^ 
Ibs.;  then  every  hundredth  of  a  foot  that  P  is  moved 
means  a  thousandth  of  a  horse-power  for  every  hundred 
revolutions. 

When  the  machine  is  not  heavy  enough  to  sink  the 
caisson  to  its  full  depth,  only  enough  water  is  put  in 
the  tank  to  just  float  the  caisson,  so  as  to  have  but 
a  thin  sheet  of  water  between  the  caisson  and  tank 
bottoms ;  this  acts  as  a  dash-pot  and  prevents  trouble- 
some oscillations.  The  exact  levelling  of  the  float  is 
completed  by  means  of  some  loose  ballast,  Z.,  and  the 


I  C>8  D  YNAMOME  TERS 

stability  is  reduced,  to  the  small  amount  required,  by 
raising  some  of  the  ballast  to  the  top  of  the  caisson  or  to 
a  (removable)  shelf t  Q,  over  the  machine.  See  Fig.  46. 

For  dynamometers  of  large  size  the  use  of  heavy 
ballast  can  be  avoided  by  the  stability-trough  K.  This 
is  a  trough  of  triangular  section  running  entirely  round 
the  inside  of  the  caisson  and  partly  filled  with  the 
same  liquid  as  is  in  the  tank  ;  by  putting  more  liquid 
in  the  trough  the  stability  is  decreased.  The  machine 
should  be  put  on  in  the  first  place  at  about  the  right 
height  ;  the  higher  it  is  the  less  the  stability.  The 
right  height  can  be  determined  by  a  simple  calculation 
of  the  centre  of  gravity  of  the  float,  but  this  is  not 
necessary,  for  the  machine  may  be  at  once  mounted 
and  blocked  up  until  the  float  shows  signs  of  insta- 
bility, when  the  final  adjustment  can  be  made  with  the 
ballast.  The  countershaft  should  then  be  blocked  up 
to  about  the  same  height.  Instead  of  setting  a  light 
machine  high  on  the  caisson  to  secure  small  stability, 
loose  ballast  can  be  put  at  once  on  the  shelf  Q  until 
the  proper  stability  is  obtained. 

By  a  suitable  arrangement  of  mechanism  upon  the 
caisson  power  may  be  transmitted  from  one  machine 
to  another,  both  standing  upon  the  floor,  and  the  ma- 
chine becomes  a  transmitting-dynamometer. 

A  very  high  degree  of  precision  can  be  attained  with 
this  dynamometer.  In  fact,  as  there  is  practically  no 
friction  in  the  liquid  to  interfere  with  the  action  of  the 
caisson,  almost  any  degree  of  precision  may  be  reached. 
Experience  has  shown  that  in  close  comparative  tests 
of  machines,  or  in  measuring  their  friction  or  air-resist- 
ance, there  is  no  other  dynamometer  with  which  the 


AArl)    THE  MEASUREMENT  OF  POWER.         10Q 

(almost  unavoidable)  accidental  errors  may  not  cover 
up  or  reverse  the  results ;  this  is  the  natural  result 
of  the  simplicity  of  principle  and  construction  of  this 
dynamometer.  The  particular  machine  illustrated  in 
the  figures  as  mounted  for  the  purpose  of  being  tested 
will  serve  as  an  illustration  of  this  fact.  In  attempting 
to  measure  the  friction  of  gearing  it  has  been  cus- 
tomary to  measure  the  power  supplied  to  the  gears  and 
that  received  from  them,  and  to  take  the  difference  of 
these  two  quantities  as  the  amount  lost  in  friction  ;  but 
the  unavoidable  error  in  measuring  these  two  quanti- 
ties by  ordinary  means  is  such  as  to  introduce  much 
uncertainty  into  the  value  obtained  for  the  friction, 
and  in  many  cases  to  render  it  entirely  valueless. 

In  explanation  of  the  particular  method  illustrated 
for  measuring  the  friction  of  gears,  it  may  be  further 
explained  that  the  lower  shaft  has  two  gears  fast  to  it, 
while  on  the  upper  shaft  the  forward  gear  is  free  to 
turn  on  the  shaft.  The  upper  gears  are  connected 
by  an  adjustable  spring,  N,  by  means  of  which  the  loose 
wheel  is  powerfully  rotated  so  as  to  bring  the  teeth  of 
the  upper  and  lower  wheels  in  contact,  with  a  known 
and  adjustable  pressure.  By  this  arrangement  it  must 
be  evident,  upon  examination,  that  the  horse-power  or 
energy  transmitted  by  the  gears  is  carried  around  in  a 
circuit  only  through  the  gears  themselves,  and  does 
not  at  all  embarrass  the  direct  measurement  of  the  loss 
due  to  friction.  The  gear  at  the  back,  or  counter- 
shaft side,  on  the  lower  shaft  drives  the  gear  above  it, 
communicating  to  it  a  certain  horse-power,  dependent 
upon  the  velocity  of  the  teeth  and  the  pressure  between 
them.  This  gear  drives  the  one  in  front  of  it  on  the 


1 1 0  D  VNA  MO  ME  TERS 

upper  shaft,  by  means  of  the  spring  N,  and  then  this 
gear  drives  the  gear  beneath  it,  thus  returning  the 
horse-power  to  the  lower  shaft,  less  the  loss  by  friction. 
The  upper  shaft  is  adjustable  on  the  standards  M. 

The  dynamometer,  therefore,  is  called  upon  to  meas- 
ure the  friction  only,  and  no  such  reliable  determina- 
tion of  frictional  losses  can  be  made  by  a  measurement 
of  gross  and  net  horse-powers,  where  the  small  quan- 
tity lost  must  be  obtained  as  the  difference  between 
the  relatively  large  gross  and  net  quantities.  This 
differential  method  of  measuring  friction  was  first  pub- 
lished by  Professor  Webb  in  the  Transactions  of  the 
American  Society  of  Mechanical  Engineers.* 

In  measuring  the  friction  and  internal  air-resistance 
of  any  machine  no  special  precautions  are  needed ; 
the  machine  is  simply  run  for  that  purpose  and  the 
measurement  made  in  the  same  way  as  any  other 
measurements  of  the  power  absorbed  by  the  machine. 
It  is,  however,  to  be  noted  that,  in  attempting  to  do 
this  with  a  dynamo,  the  residual  magnetism  will  cause 
a  waste  of  power  in  Foucault  currents,  which  will  be 
included  in -and  may  invalidate  the  measured  result. 
This  residual  magnetism,  however,  may  be  nearly 
eliminated  by  means  of  a  current  from  a  battery,  or 
from  another  machine,  which  is  passed  through  the 
field  and  successively  reversed  and  reduced  by  means 
of  a  rheostat.  There  is  no  way  of  separating  the  in- 
ternal air-resistance  from  the  friction,  except  to  get 
rid  of  it  by  running  the  machine  in  vacuo. 

If  it  be  the  external  air-resistance  or  "  fanning"  that 

*Vol.  ix.  p.  213. 


AND    THE  MEASUREMENT  OF  POWER.        Ill 

is  in  question,  the  machine  is  to  be  run  as  a  motor,  the 
belt  having  been  removed,  and  the  measurement  is  to 
be  made  in  the  same  way  as  before,  but  with  a  degree 
of  care  suited  to  the  small  quantity  to  be  determined. 

A  dynamometer  for  measuring  40  to  50  H.  P.  occu- 
pies, without  the  countershaft,  a  floor-space  of  about 
ninety  inches  square,  and  may,  if  desired,  be  built 
beneath  the  floor,  so  as  to  have  the  general  appearance 
and  convenience  of  platform-scales. 

A  patent  has  been  applied  for  upon  the  Floating 
Dynamometer. 

In  the  experiments  of  Hartig  a  dynamometer  was 
used  in  which,  by  means  of  a  series  of  gears,  the  rotat- 
ing force  is  made  to  act  upon  a  pair  of  springs,  one  of 
which*  is  furnished  with  a  pencil  which  describes  a  curve 
as  a  roll  of  paper  is  caused  to  move  before  it.  The 
principle  of  action  will  be  understood  from  the  follow- 
ing, which  is  abstracted  from  Weisbach's  Mechanics.* 

To  the  interior  of  the  wheel  CA,  Fig.  48,  upon  which 
the  rotating  force  P  acts  at  A,  is  bolted  an  annular 
gear  which  engages  at  D  and  D^  with  two  equal  gears, 
DE  and  D^E,  both  of  which  act  upon  a  third  gear, 
EE.  This  last  gear  revolves  freely  upon  the  shaft  C 
of  the  wheel  DDt ,  and  is  firmly  attached  to  the  drum 
BC  upon  which  the  resistance  Q  acts,  while  the  other 
two  gears,  DE  and  D^E,  have  their  axes  supported  by 
a  lever,  FCFl ,  which  revolves  freely  about  C.  On  the 
hub  of  this  lever  is  a  band,  one  end  of  which  is  fast- 
ened to  the  dynamon>eter-springs  H  H,  which  latter  are 
bolted  at  M  to  the  floor.  We  see  that  here  the  rotat- 

*  Dubois*  translation,  vol.  n.  part  I. 


115  D  YNA  MOME  T£JtS 

ing  force  P  is  held  in  equilibrium  by  two  forces,  R  and 
—  R,  that  out  of  these  last  arises  a  couple,  —R,R, 
which  holds  the  force  of  resistance  Q  in  equilibrium,  and 
that  therefore  the  forces  2.R  and  —  2R  act  at  F  and  /'", 
and  stretch  the  springs  H  H  with  a  certain  force  Z. 


FIG.  48. — ARRANGEMENT  USED  BY  HARTIG. 

Let  a  =  lever-arm  CA  of  the  force  P\ 

b  =  lever-arm  CB  of  the  resistance  Q  ; 
r  =  radius  CD  of  large  annular  gear  ; 
rl  =  radius  CE  of  centre  gear-wheel,  and  hence 

— ——  —  radius  FD  of  intermediate  gear, 

c  =  lever-arm  of  the  force  Z  —  CL. 
Then  we  shall  have 

Pa  -  Rr  =  Rr,     or    Pa  =  2Rr ; 


AND    THE  MEASUREMENT  OF  POWER.         113 
also, 


Qb  =  2Rr,  ,     and     Zc  —  Qb  =  Pa. 
Substituting  above  values  for  Qb  and  Pa,  we  have 


hence 


and 


Pa  _  2Rr  P  _  b_      r_ 

~~  ~~  * 


Pa  2Rr  P      c  ^ 

—  -,     or     —  =  -  X 


Zc       2K(r+rty  Z      «      r-j-r, 


Among  other  forms  of  dynamometer  not  already 
discussed  is  the  Emerson  Power-scale  —  an  instrument 
which  is  connected  directly  to  the  revolving  shaft  with- 
out the  interposition  of  belts,  except  that  used  to  drive 
the  shaft  itself.  The  machine  in  principle  is  a  rotary 
scale,  and  its  construction  closely  resembles  the  well- 
known  Fairbanks  platform-  scales.  This  dynamometer 
is  largely  used  in  cotton-mills  to  determine  the  power 
consumed  by  the  individual  machines,  and  when  used 
with  care  forms  an  excellent  instrument  for  the 
purpose,  being  self-contained  and  readily  applied.  In 
this  machine,  the  pulley  which  receives  the  power  is 
loose  on  the  shaft,  and  is  connected  with  the  latter  by 
means  of  a  spider  which  is  keyed  to  the  shaft,  the  hub 
of  the  spider  forming  one  of  the  guides  to  the  position 
of  the  pulley  (not  shown  in  the  figure);  to  connect  this 
spider  with  the  loose  pulley,  a  lever  is  pivoted  into  lugs 
on  the  rim  of  the  wheel  on  opposite  sides,  the  long  arm 
of  which  connects  with  an  annular  slotted  collar  on  the 
shaft  by  means  of  short  links. 


114  D  YNAMOME  TERS 

The  short  arms  of  the  crank-levers  connect  on  the 
inside  of  the  fixed  wheel  with  two  radial  links,  one 
parallel  to  the  outer  arm  of  the  bell-crank,  and  the 
other  at  right  angles  to  it,  receiving  at  its  upper  end  a 
pivot  passing  through  a  swivel  hung  to  the  arm  of  the 
spider-wheel,  and  having  its  extreme  end  pivoted  to  a 
stud  fixed  on  the  inner  side  of  the  rim  of  the  receiving 
pulley.  The  strain  of  the  power  received  through 
the  belt  on  the  pulley  will  necessarily  react  on  the 
levers,  and,  through  them,  on  the  spider,  which  may 
be  considered  as  a  support  to  these  levers  in  sustaining 
them  in  position  to  connect  the  loose  receiving  pulley 
with  the  shaft.  The  levers  are  connected  by  pivots 
with  the  sliding  collar,  in  the  annular  groove  of  which 
is  seated  a  strap  with  which  is  connected  a  forked  lever. 
Attached  to  the  end  of  the  long  arm  of  this  lever  is  a 
rod  carrying  movable  weights ;  connected  with  this 
rod  is  a  chain  which  runs  over  the  cylindrical  head  of 
a  pendulum-weight  having  a  pointer  which  traverses  a 
fixed  quadrant:  this  quadrant  being  divided  by  a  scale 
to  denote  the  relative  pressure  exerted  through  the 
medium  of  the  receiving  pulley  on  the  shaft.  A  dash- 
pot  filled  with  oil  is  connected  to  the  long  lever  and 
chain-rod  to  prevent  unnecessary  oscillations  of  the 
pendulum.  These  instruments  are  made  in  halves,  so 
that  they  may  be  readily  applied  without  disarranging 
pulleys  or  line-shafting. 

The  cotton-mill  scale  shown  in  Fig.  49  is  fitted  with 
special  clutch  and  split  bushings  to  fit  shafts  varying 
from  f  inch  to  i^  inches,  being  secured  in  position  by 
nut  B.  In  this  form  of  scale  two  sets  of  prime  levers, 
K  K,  are  used,  so  as  to  operate  without  change  when 


AND    THE  MEASUREMENT  OF  POWER.         115 

running  in  either  direction.  Two  studs,  one  of  which 
is  shown  at  C,  are  used  to  connect  the  loose  driving 
pulley  with  the  spider  which  is  keyed  to  the  shaft.  These 


FIG.  49. — EMERSON  POWER-SCALE. — Oc 


studs  are  screwed  into  a  plate  with  projecting  lug 
which  drives  the  spider  by  means  of  the  pin  G  in  the 
rim.  When  the  slide  H  is  pushed  in  as  shown  in  thr 


1 16  D  YNAMOME TERS 

figure,  the  stop  G  is  thrown  out  of  gear  with  the  loose 
plate,  and  this  latter  is  free  to  revolve  on  the  hub  of 
the  spider,  being  driven  by  the  loose  pulley. 

These  scales  are  constructed  so  that  the  pivots  in 
the  ends  of  the  levers  at  L  describe  a  circle  whose 
circumference  is  two  feet,  and  the  quadrants  are  gradu- 
ated to  read  pounds  ;  if  the  graduations  are  insufficient, 
weights  may  be  added  at  J,  the  leverage  of  the  scales 
being  such  that  an  actual  weight  of  one  pound  placed 
at  J  has  the  effect  of  fifty  pounds  on  the  quadrant. 

In  the  larger  power-scales  the  centre  of  pivots  of 
the  prime  levers  (K)  is  always  taken  at  such  a  distance 
from  the  centre  that  the  distance  passed  through  in 
one  revolution  is  equal  to  a  given  number  of  feet. 
Thus  in  the  scale  designed  to  weigh  65  horse-power, 
the  greatest  diameter  of  the  machine  is  38  inches  and 
the  space  passed  through  by  pivot  L  in  one  revolution 
is  9  feet. 

To  ascertain  the  number  of  horse-power  by  means 
of  an  Emerson  power-scale  it  is  first  necessary  to  find 
the  centrifugal  force  of  the  unbalanced  moving  parts 
of  the  scale.  This  is  obtained  by  running  the  belt  on 
the  tight  pulley,  the  loose  plate  being  disconnected 
from  the  spider,  then  note  the  reading  as  shown  by 
the  position  of  the  pendulum  on  the  quadrant. 

This  amount  will  be  small  for  slow  speeds,  and  below 
a  certain  minimum  speed  will  be  zero ;  but  as  it  varies 
with  the  square  of  the  number  of  revolutions,  it  should 
in  every  case  be  determined  at  the  same  velocity  at 
which  the  total  force  is  determined.  In  a  test  by  Mr. 
Channing  Whitaker  to  determine  the  effect  of  a  cotton- 
mill  scale  it  was  found  that  at  a  speed  of  416  revolu- 


AND    THE  MEASUREMENT  OF  POWER.         ll'J 

tions  per  minute  the  reading  was  one-half  pound,  but 
at  the  speed  of  1000  revolutions  per  minute  it  amounted 
to  thirty-six  pounds. 

Having  ascertained  the  amount  to  be  deducted  for 
a  given  speed,  which  is  in  fact  equivalent  to  balancing 
the  scale,  we  can  find  the  horse-power  developed  from 

PV 
our  general  formula  ---  =  H.P. 

If  f  =  total  pounds  indicated  on  the  quadrant, 
_/"=  pounds  necessary  to  balance  at  given  speed, 
N  '=  number  of  revolutions  per  minute, 
C  =  path  in  feet  of  end  of  lever  (X), 
then 

F  —  f=P,     and     N  X  C  =  V, 

which  substituted  in  above  formula  will  give  net  horse- 
power. The  observed  data  of  a  test  with  a  cotton-mill 
scale  was  as  follows  : 

The  gross  indicated  force  =  83  pounds;  the  tare  or 
balancing  force  =  23  pounds;  revolutions  per  minute 
=  791.  The  path  of  end  of  lever  being  2  feet,  we  obtain 

(83-23)791  X  2 

=  2'87  horse-power. 


Another  form  of  shaft-dynamometer  is  the  Power- 
meter  which  has  recently  been  patented  by  Mr. 
Franklin  Van  Winkle.  This  is  a  rotary  transmitting- 
dynamometer  which  is  especially  adapted  for  adjust- 
ment to  any  shaft  or  pulley  for  measuring  power 
transmitted  by  a  shaft  to  a  pulley,  or  vice  -versa,  in  this 
respect  resembling  the  Emerson  power-scale. 


n8 


D  YNAMOME  TERS 


Helical  pull-springs  are  employed  for  weighing  the 
amount  of  force  transmitted  from  the  driving  to  the 
driven  portion  of  the  dynamometer. 

Figs.  50-58  will  illustrate  the  construction  and  ap- 
plication of  this  dynamometer. 

Figs.  50-55  are  illustrative  more  particularly  of  the 
"light  portable  "  style.  The  construction  and  opera- 


FIG.  50. 

tion  of  all  other  styles  will,  however,  be  understood 
from  this  description,  as  it  embraces  the  features  of  the 
others. 

Similar  letters  refer  to  similar  parts  throughout  the 
I  several  views. 


To  facilitate  the  application  of  the  dynamometer  to 
a  shaft,  the  main  framework  and  all  parts  which  sur- 
round the  shaft  are  made  in  halves,  in  order  that  the 
dynamometer  may  be  mounted  on  the  shaft  in  the 
manner  of  a  split  or  separable  pulley. 


AND    THE  MEASUREMENT  OF  POWER.         I  ig 

Split  bushings  are  used  for  reducing  the  bore  on  any 
shaft  smaller  than  the  hole  in  the  hub.  For  bushing 
machines  employing  four  springs  it  is  immaterial 
whether  or  not  the  machine  is  concentric  with  the 
shaft ;  hence  rough  wood-bushings  may  be  employed. 


The  main  hubs  of  all  machines  are  chambered  in  the 
middle  of  their  length,  in  order  to  leave  room  for  cord 
to  be  tied  around  the  outside  of  wood  bushings  or  lag- 
ging of  any  kind  that  is  convenient  for  building  up 
the  size  of  the  shaft.  Thin  manila  drawing-paper 
wrapped  around  the  shaft  answers  the  purpose  admir- 
ably. 

The  main  framework  consists  in  an  elliptical  plate 


I2O 


D  YNAMOME  TERS 


B,  the  outline  of  which  is  best  shown  in  Fig.  51. 
This  plate  has  a  central  hub  C,  prolonged  on  one 
side,  with  the  grooved  collar  e  near  its  end ;  this 
hub  projects  a  short  distance  to  the  other  side  of 
the  plate,  with  a  spherical  exterior  surface  D  (see 
Figs.  52  and  53)  terminating  in  the  plain  collar  E, 
the  plate  and  hubs  being  made  in  halves  and  held 
together  by  bolts  passing  through  the  projecting  lugs 


FIG.  52. 

G  G.  The  central  hollow  hub  of  this  main  framework 
is  recessed  along  a  portion  of  its  prolonged  end  and 
bored  out  in  the  remaining  portions  of  its  length  to  re- 
ceive the  shaft  upon  which  it  may  be  placed,  as  shown 
in  Fig.  53. 

A  is  a  circular  plate  the  middle  portion  of  which  is 
dished  or  crowning.  This  plate  is  made  in  halves 
coming  together  along  the  line  HH,  Fig.  51,  and  held 
together  by  bolts  passing  through  projecting  lugs  //, 
Fig.  50,  the  plate  being  provided  with  a  short  central 
hollow  hub  which  is  bored  out  to  fit  loosely  around 


• 
AND    THE  MEASUREMENT  OF  POWER.         121 

the  spherical  portion  D  of  the  central  hub  of  the  main 
framework. 

AT  is  a  rock-shaft  the  ends  of  which  have  counter- 
sunk recesses,  by  means  of  which  it  is  mounted  on 
conically-pointed  screws  L  L,  which  pass  through  lugs 
projecting  from  B  and  are  held  firmly  in  place  by 
lock-nuts  MM.  N  is  an  arm  on  AT  projecting  toward 
the  plate  A,  and  o  and  o  are  parallel  arms  projecting 
from  K  at  right  angles  to  N,  one  over  each  side  of  the 
hub  C. 

P  P  are  links  connecting  by  pivotal  screws  the 
ends  of  the  parallel  arms  o  o  to  the  grooved  collar  Q, 
which,  being  made  in  halves,  encircles  the  reduced  por- 
tion of  hub  C,  being  free  to  slide  along  C,  and  provided 
with  feathers  which  project  into  the  slots  S,  Fig.  52. 

T  is  a  connecting-rod  having  spherical  socket-ends 
with  detachable  caps. 

U  and  U'  are  spherical  or  ball-ended  stud-bolts  set 
in  the  end  of  the  arm  N,  and  in  the  curved  slot  x  in 
the  plate  A,  respectively,  and  connected  by  the  con- 
necting-rod T  (see  Fig.  51).  When  the  plate  A,  rock- 
shaft  K,  and  collar  Q  are  mounted  on  the  framework 
of  the  dynamometer  and  connected  as  described,  then 
any  change  of  relative  angular  position  between  the 
plates  A  and  B  around  the  axis  of  hub  C  will  cause  Q 
to  move  along  the  hub,  the  direction  and  degree  of 
travel  being  dependent  upon  the  relative  direction  and 
degree  of  motion  between  the  two  plates  A  and  B. 

V  V  are  bosses  on  one  side  of  the  plate  A,  project- 
ing toward  B.  X  is  a  similar  boss  on  the  plate  B, 
projecting  toward  the  plate  A. 

IV,   Fig.  51,  is  a  helical  pull-spring  connecting  the 


122 


DYNAMOMETERS 


plates  A  and  B.  The  material  of  the  helix  forming  W 
is  turned  up  in  eyes  at  both  ends,  through  which  the 
suspending  pins  Kand  Y'  pass,  the  pins  being  held  in 
place  by  set-screws,  as  shown  in  Fig.  53.  If  the  plate 
A  be  rotated  on  its  axis  in  the  direction  indicated  by 


FIG.  53. 

the  arrow  Z,  Fig.  51,  any  resistance  offered  to  such 
rotation  by  B  will  be  transmitted  through  W  to  A, 
causing  W  to  elongate,  and  thereby  permitting  A  to 
advance  in  its  relative  angular  position  with  respect  to 
B  in  direction  of  the  arrow  Z  until  the  resistance 
offered  by  B  is  overcome  by  W.  Then  B  follows  along 
in  the  rotation  primarily  imparted  to  A.  The  direc- 
tion of  arrow  c  in  Figs.  52  and  54  is  the  same  with 
respect  to  B  as  arrow  Z  in  Fig.  51.  Consequently, 


AND    THE  MEASUREMENT  OF  POWER.         12$ 

when  A  advances  in  rotation  with  respect  to  B  in  the 
manner  described  and  the  ball-stud  U'  is  fixed  in  the 
slot  x  of  the  plate  A,  then  U',  T,  and  U  and  the  end 
of  the  arm  TV  are  carried  in  direction  of  arrow/,  im- 
parting a  partial  revolution  of  the  shaft  K  on  its  axis, 
resulting  finally  in  movement  of  the  parallel  arms  o, 
links  P,  and  collar  Q  in  direction  of  arrow  d.  If,  dur- 
ing such  rotation  of  A,  the  resistance  offered  by  B 
lessens,  then  the  spring,  by  reason  of  transmitting 
a  lesser  strain,  resiles  to  such  length  as  may  cor- 
respond to  the  reduced  resistance  and  carries  B  for- 
ward in  the  direction  of  rotation  toward  its  original 
position  with  respect  to  A.  Each  particular  degree  of 
resistance  transmitted  by  the  spring  from  one  plate  to 
the  other  produces  its  particular  position  of  the  sliding 
collar  Q  on  the  hub,  and  will  be  indicated  upon  the 
scale  by  the  pointer  »,  as  follows : 

In  Fig.  50  /  and  g  are  rings  made  in  halves,  the  in- 
terior surfaces  of  which  are  suitably  bevelled  for  fitting 
loosely  around  the  grooves  in  the  sliding  collar  Q  and 
fixed  collar  e.  These  rings  are  each  provided  with  two 
bosses  for  the  purpose  of  receiving  the  guide-rods  /  /', 
one  end  of  each  being  screwed  into  g,  while /"is  free  to 
slide  over  the  remaining  portion  of  the  rods.  The  ring 
f  has  a  projection  /,  see  Figs.  54  and  55,  to  which  is 
pivoted  the  link  k,  and  the  ring  g  has  projecting  from  it 
the  scale-plate  /,  the  lower  portion  of  which  is  made  in 
form  of  a  segmental  arc,  on  which  is  laid  off  a  scale. 

In  Fig.  54  «  is  a  pointer-hand  pivoted  at/  and  con- 
nected by  the  link  k  to  the  ring/",  its  free  end  being 
carried  over  the  scale  in  accordance  with  the  motion 
of  the  ring  f,  in  the  sliding  collar  Q  along  the  hub- 


124  DYNAMOMETERS 

When  the  hub  is  in  rotation,  the  scale-rings  f  and  g 
may  be  prevented  from  rotating  with  the  hub,  and 
caused  to  remain  stationary  by  holding  the  downward, 
extending  portion  of  the  scale-plate  in  the  hand,  or  by 
securing  the  lower  portion  of  the  scale-plate  by  twine 
or  otherwise  to  a  stationary  object.  The  position  as- 
sumed by  the  pointer-hand  on  the  scale  may  be  noted 
while  the  hub  is  in  rotation. 

If  the  plate  B  receives  the  primary  rotation  instead 
of  A,  but  in  a  direction  opposite  to  that  indicated  by 
the  arrow  Z,  Fig.  51,  and  such  rotation  be  resisted  by 
the  plate  A,  then  the  spring  JFwill  be  similarly  elon- 
gated, and  n  will  be  carried  over  the  scale  in  the  same 
manner. 

The  periphery  of  the  plate  B  has  cut  out  of  it 
a  gap  or  notch  bounded  by  projecting  lugs  q  and 
r,  through  which  pass  the  set-screws  s  and  /.  u  is 
the  stop-bracket  projecting  from  the  plate  A  through 
the  gap  in  B.  When  the  spring  in  its  normal  length 
and  without  any  strain  upon  it  connects  A  and  £, 
as  previously  described,  then  A  is  to  be  turned  past 
B  sufficiently  to  take  up  any  lost  motion  between  the 
suspending  pins  and  the  plates  A  and  B  or  between 
the  suspending  pins  and  the  eyes  of  the  spring. 
The  screw  s  is  then  to  be  set  down  and  secured  in  con- 
tact with  n.  With  u  and  s  thus  in  contact  the  dyna- 
mometer may  be  driven  backward  without  injury  to  or 
derangement  of  its  parts.  When  driven  in  the  direc- 
tion which  tends  to  elongate  the  spring,  the  maxi- 
mum relative  motion  between  the  two  plates  and 
consequently  the  maximum  elongation  of  the  spring 
are  both  limited  by  u  coming  in  contact  with  the 


AND    THE  MEASUREMENT  OF  POWER.         12$ 

end  of  the  screw  /.  If,  however,  it  be  desired  to 
measure  resistance  transmitted  between  the  plates 
when  the  relative  directions  of  rotation  are  opposite  to 
those  described,  then  in  order  that  such  resistance 
may  be  transmitted  in  a  manner  tending  to  elongate 
W  it  is  necessary  for  W  to  be  connected  from  the  pro- 
jecting hub  X  of  the  plate  B  to  the  projecting  hub  V 
of  the  plate  A  by  means  of  the  suspending  pins  Fand 
Y"  When  the  spring  is  connected  without  strain,  as 
shown  in  Fig.  51,  the  proportions  of  the  dynamometer 
are  such  that  the  distance  from  X  to  V  is  greater  than 
the  distance  from  X  to  V  by  such  an  amount  that  in 
order  to  connect  W  without  strain  from  X  to  V  it  is 
first  necessary  to  rotate  A  around  B  in  the  direction  of 
arrow  Z  a  sufficient  distance  to  bring  the  side  of  the 
stop-bracket  u  against  the  end  of  /.  t  is  then  in  posi- 
tion to  operate  as  a  backward  stop,  while  s  becomes  the 
forward  stop.  When  W  is  thus  changed  about,  the 
partial  rotation  of  A  past  B,  which  is  incidental  there- 
to, results  in  carrying  the  pointer-hand  to  a  point  to 
the  left  of  the  zero  of  the  scale — that  is  to  say,  in  di- 
rection of  the  arrow  d.  The  pointer-hand  may  be  re- 
turned to  zero  by  loosening  the  ball-stud  V '  in  the 
slot  x  of  the  plate  A  and  moving  it  along  the  slot  to 
such  position  that  n  again  indicates  zero,  in  which 
position  U'  may  be  again  secured  to  A.  When  thus 
adjusted,  any  resistance  to  rotation  between  the  plates 
A  and  B,  causing  the  spring  to  elongate,  will  cause  n 
to  assume  a  position  to  the  right  of  the  zero  of  the 
scale. 

Successive  positions  which  the  end  of  the  pointer- 
hand  n  will  assume  on  the  arc  of  the  scale-plate  for 


126  D  YNA  MO  ME  TERS 

different  numbers  of  horse-powers  or  foot-pounds  per 
minute  transmitted  from  A  to  B  or  B  to  A,  employ- 
ing a  given  spring,  may  be  determined  for  a  given 
speed  of  rotation  of  the  dynamometer,  inasmuch  as 
the  degree  of  elongation  of  the  spring  is  ascertainable 
for  any  degree  of  resistance  to  rotation  which  the  plate 
A  may  offer  to  the  plate  B,  or  vice  versa.  Thus  if  the 
distance  from  centre  of  shaft  to  centre  of  the  suspend- 
ing pins  of  the  spring  W  be  5  inches,  and  the  elonga- 
tion of  the  spring  be  I  inch  under  a  pull  of  200  pounds, 
the  horse-power  transmitted  at  100  revolutions  per 
minute  for  an  elongation  of  half  an  inch  will  be 

jr  D         2lRNP        27T  X  5   X    100  X    100 

fl.r.  = = = =  Q.  15  2. 

33000  33000 

For  a  given  extension  of  the  spring,  which  represents 
a  corresponding  force  P,  the  pointer-hand  will  assume 
a  definite  position,  and  if  the  lever-arms  of  the  instru- 
ment be  suitably  proportioned,  the  arc  may  be  so 
graduated  that  for  a  given  spring  the  successive  divi- 
sions will  represent  horse-powers  and  decimals  for  a 
fixed  number  of  revolutions  per  minute.  Fig.  50  illus- 
trates the  appearance  of  a  divided  and  figured  scale 
laid  off  on  /  in  the  manner  described  for  a  stated  speed 
of  rotation  of  the  dynamometer — as,  for  instance,  one 
hundred  revolutions  per  minute — using  always  the 
same  spring.  In  dynamometers  heretofore  made  this 
has  been  the  only  type  of  scale  provided,  and  when 
such  a  scale  is  used  at  any  other  speed  of  rotation,  or 
when  any  change  is  made  in  the  spring  employed  dif- 
ferent from  those  for  which  the  scale  is  especially  con- 


AND    THE  MEASUREMENT  OF  POWER.         12? 

structed,  then,  in  order  to  arrive  at  the  true  number  of 
horse-powers,  the  operator  must  make  calculations  for 
every  reading. 

To  obviate  this  the  Van  Winkle  dynamometer  is 
provided  with  a  "differential"  scale-plate  by  which  the 
horse-power  for  varying  speeds  is  indicated  directly 


FIG.  54— DIFFERENTIAL  SCALE-PLATE. 


by  the  pointer,  within  the  limits  of  the  spring  used. 
This  consists  of  a  flat  spade-shaped  plate  d'  of 
form  shown  in  Fig.  54,  the  narrow  upper  portion  of 
which  has  parallel  slotted  openings  e' .  The  differen- 
tial plate  when  used  is  to  be  laid  upon  the  face  of  / 
under  the  pointer-hand,  as  shown,  and  may  be  secured 
in  different  positions  of  vertical  adjustment  by  means 
of  screws  f'f,  which  pass  through  the  slots  into  the 


128  D  YNAMOME  TERS 

upper  part  of  /.  When  using  always  the  same  spring 
or  equal  springs,  arbitrarily-spaced  lines,  each  repre- 
sentative of  a  speed  of  rotation,  are  made  upon  the 
face  of  the  upper  portion  of  /  in  form  of  a  scale  g',  and 
so  laid  off  that  the  upper  edge  of  d'  may  be  brought 
opposite  to  any  division  on  g' .  As  shown  in  Fig. 
54,  the  face  of  d'  is  laid  off  with  a  central  zero- 
line,  to  the  right  and  left  of  which  are  curved  lines 
marked  "1,2,  3,  4,"  etc.  These  "  differential  curves  " 
are  of  such  form  that  when  the  upper  edge  of  d'  is  set 
opposite  to  that  division  of  g'  corresponding  to  any 
given  speed  of  rotation  made  by  the  dynamometer, 
then  the  end  of  the  pointer-hand  will  be  on  the  curve 
marked  "  I  "  when  one  horse-power  is  being  trans- 
mitted, on  curve  "  2  "  for  two  horse-powers,  "  3  "  for 
three  horse-powers,  etc.,  to  the  right  or  left  of  the  zero- 
line,  according  to  the  direction  of  resistance  for  which 
the  spring  and  pointer-hand  may  have  been  adjusted. 

When  the  dynamometer  is  always  to  be  used  at 
a  constant  speed  of  rotation  and  for  the  purpose 
of  greater  or  less  sensitiveness  of  action,  different 
strengths  of  springs  are  employed  at  different  times. 
Then  in  a  similar  manner  the  differential  scale-plate 
may  be  laid  off  in  curves  to  be  used  for  indicating 
different  horse-powers,  the  divisions  of  the  scale  g'  be- 
ing then  taken  as  representative  of  different  strengths 
of  springs  instead  of  different  speeds  of  rotation. 

For  springs  offering  different  degrees  of  resistance 
to  elongation,  each  of  which  may  be  used  in  the  dyna- 
mometer at  different  speeds  of  rotation  of  the  latter, 
the  same  general  form  of  differential  scale-plate  is 
employed  in  conjunction  with  the  compounding  scale- 


AND    THE  MEASUREMENT  OF  POWER. 


I29 


plate  y,  Fig.  55.  The  scale-divisions  g'  are  then  dis- 
carded, excepting  a  single  division-line  k',  which,  for 
greater  explicitness  of  location,  is  marked  with  an 
arrow-head.  By  means  of  the  binding-screw  k! ',  which 
passes  through  the  slotted  projecting  portion  of  the 


FIG.  55 — COMPOUNDING  SCALE-PLATE. 

back  of  /',  the  latter  may  besecured  in  different 
vertical  adjustments  with  reference  to  /,  so  that  any 
one  of  the  division-lines  drawn  on  the  face  of  j'  may 
be  opposite  to  h' . 

Beginning  at  a  certain  division  on  j',  as,  for  exam- 
ple, that  marked  "  loo,"  and  proceeding  upward,  lines 
are  drawn  each  of  which  is  representative  of  the  num- 
ber of  pounds  required  to  elongate  different  springs 


I  30  D  YNAMOME  TERS 

I  inch,  as  one  hundred,  two  hundred,  three  hundred, 
etc.;  and  similarly  beginning  at  "  100"  on/'  and  pro- 
ceeding downward,  lines  are  drawn  representative  of 
different  speeds  of  rotation  of  the  dynamometer,  as, 
for  instance,  one  hundred,  two  hundred,  three  hundred, 
etc.,  revolutions  per  minute. 

The  spacings  of  the  divisions  of  the  compounding 
scale-plate  j'  and  the  curves  on  the  differential  scale- 
plate,  when  used  in  conjunction  with  the  compounding 
scale,  are  such  that  the  pointer-hand  will  indicate  the 
correct  number  of  horse-powers  on  the  differential 
scale-plate  provided  j'  is  so  adjusted  that  the  division 
representing  the  strength  of  spring  employed  is  oppo- 
site the  division-line  //'  marked  with  an  arrow-head, 
and  the  upper  edge  of  d'  is  fixed  opposite  to  that  divi- 
sion on/'  representing  the  speed  of  rotation. 

In  order  to  apply  the  dynamometer,  as,  for  instance, 
for  the  purpose  of  measuring  the  horse-power  taken  by 
a  pulley  /',  Fig.  53,  from  line-shaft  c',  the  pulley  is 
first  loosened  from  the  shaft  by  removing  set-screws, 
keys,  or  other  means  of  fastening,  making  of  it  a  loose 
pulley.  A  short  distance  one  side  or  the  other  of  the 
pulley  the  plate  B  is  mounted  on  the  shaft,  the  halves 
being  secured  together  by  the  bolts  through  lugs  G. 
Then  the  rock-shaft  K  and  its  connections,  the  scale- 
ring  and  scale  employed,  and  finally  the  plate  A  are 
all  mounted  on  B.  The  weighing  spring  W  is  then 
connected  according  to  the  direction  of  motion,  and 
the  ball-stud  U'  is  set  in  the  slot  x,  so  as  to  bring  the 
pointer  n  to  indicate  zero  when  the  stop-bracket  u  is 
against  the  end  of  the  screw  s  or  t  for  a  back-stop. 
The  dynamometer  is  then  moved  along  the  shaft  until 


AND    THE  MEASUREMENT  OF  POWER.         131 

the  periphery  of  the  plate  A  comes  against  the  arms 
of  the  pulley.  The  periphery  of  A  has  a  projecting 
surfacejj/',  which  is  perforated  all  around  by  holes,  as 
shown  in  Fig.  51.  The  plate  A  is  secured  to  the  pul-* 
ley  by  means  of  bolts  and  straps  which  pass  over  the 
arms.  The  plate  B  is  then  secured  to  the  shaft  by  the 
set-screw  S'  (shown  in  Figs.  51  and  52).  When  the 
shaft  is  set  in  motion,  any  power  taken  from  it  by  the 
pulley  for  driving  other  machinery  by  means  of  a  belt 
will  be  transmitted  from  the  plate  R  to  the  pulley 
through  the  spring  W,  resulting  in  a  greater  or  less 
elongation  of  W,  and  consequent  movement  of  the 
pointer-hand  to  a  position  on  the  scale-plate  employed, 
and  the  latter,  as  previously  noted,  may  be  held  sta- 
tionary or  secured  to  a  stationary  object  to  prevent  its 
turning  with  the  dynamometer. 

It  will  be  noticed  that  the  performance  of  the  weigh- 
ing springs  is  transmitted  by  positive  mechanism  to 
the  pointer-hand  on  the  dial ;  no  wrapping  connectors 
of  any  kind  being  employed. 

The  Light  Portable  style  weighs,  complete,  62^  Ibs., 
and,  as  intimated  in  the  description,  it  is  supplied 
with  springs  of  different  degrees  of  sensitiveness,  up  to 
a  capacity  of  20  horse-power  at  100  revolutions  per 
minute. 

Another  form  of  the  Van  Winkle  dynamometer  has 
two  or  more  springs  similarly  connected  in  a  series. 
The  pins  for  suspending  the  weighing  springs  are  the 
same  distance  apart  and  at  a  uniform  distance  from  the 
axis  of  the  dynamometer.  One  of  the  springs  operates 
the  same  as  the  single  spring  employed  in  the  Light 
Portable  style,  taking  up  the  load  from  the  beginning. 


132  D  YNAMOME  TERS 

This  is  called  the  initial  weighing  spring.  The  remain- 
ing springs  have  looped  eyes  at  one  end,  the  loops 
being  of  such  different  lengths  that  after  the  initial 
spring  has  been  loaded  to  a  portion  of  its  capacity  the 


FIG.  56— VAN  WINKLE  Dv 


looped  springs  assist  the  initial,  drawing  on  their  sus- 
pending pins,  one  after  another. 

This  system  of  suspending  the  weighing  springs 
greatly  facilitates  accuracy  in  construction,  application, 
and  use  of  the  dynamometer. 

The  holes  for  the  suspending  pins  being  equally 
spaced,  the  springs  are  interchangeable  in  location  ;  and 


A.VD    THE  MEASUREMENT  OF  POWER. 


133 


the  amplitude  of  swing,  or  change  of  relative  angular 
position  between  the  plates,  being  dependent  upon  the 
resistance  of  only  one,  or  as  many  springs  as  may  be 
necessary  for  transmitting  any  load,  the  divisions  of 
the  zero  end  of  the  scale  are  coarser  than  if  all  springs 
started  to  pull  at  the  beginning,  and  admit  of  smaller 
fractional  sub-division. 

Still  another  form  is  shown  in  Figs.  56,  57,  and  58, 
in  which  A  is  the  pulley-plate  and  B  the  plate  which  is 


FIG.  57. 

secured  to  the  shaft.  It  differs  from  the  Light  Port- 
able style  in  requiring  the  connecting-rod,  which  oper- 
ates the  rock-shaft,  to  be  changed  to  the  other  side  of 
the  machine,  in  order  to  use  the  dynamometer  in  a 
reverse  direction  :  and  the  weighing  springs  being  sus- 
pended from  stud-bolts,  the  springs,  together  with 
their  stud-bolts,  must  be  removed  from  the  plates  A 
and  By  and  the  studs  inserted  each  in  the  opposite 
plate  in  holes  provided  for  the  purpose. 

Fig.  57  illustrates  the  parts  of  the  "  Standard  Port- 
able" dynamometer,  and  Fig.  58  illustrates  it  applied 
to  a  shaft  and  pulley. 


134 


D  YNAMOME  TERS 


It  is  claimed  by  the  manufacturer  that  these  dyna- 
mometers are  only  about  one-half  the  weight  of  other 
types  for  equal  capacities.  The  dynamometers  have 
been  tested  after  several  years'  use  and  the  weighing 
springs  have  been  found  to  retain  their  original 
strength. 

No   allowance    for   centrifugal,    frictional,   or   other 


FIG.  58— VAN  WINKLE  DYNAMOMETER  APPLIED  TO  SHAFT. 

error  is  made  in  using  this  instrument.  The  weighing 
springs  are  so  proportioned  that,  as  has  been  proven 
in  tests  of  the  dynamometer,  the  indications  of  the 
scale  are  unaffected  by  centrifugal  disturbance  beyond 
the  highest  speeds  of  shaft  in  practice. 

The  transmitting  mechanism  is  so  proportioned  and 
balanced  that  any  tendency  to  centrifugal  disturbance 
is  avoided. 

The  only  sources  of  frictional  disturbance  are  in  the 


AND   THE  MEASUREMENT  OF  POWER.         135 

pivotal  joints  of  the  rock-shaft  motion  and  the  friction 
due  to  the  weight  of  the  scale.  When,  however,  the 
dynamometer  is  employed  for  measuring  the  amount 
of  power  which  a  pulley  receives  from  a  shaft,  then  this 
small  amount  of  friction  is  not  thrown  on  the  weighing 
springs. 

There  is  no  friction  between  the  pulley  and  the  shaft, 
nor  between  that  portion  of  the  dynamometer  which  is 
secured  to  the  pulley  and  the  rest  of  the  instrument. 
This,  at  first  sight,  may  not  appear  to  be  the  case ; 
tests  of  the  dynamometer  show,  however,  that  no  fric- 
tion exists  in  cases  where  the  pulley  when  loosened 
from  the  shaft  is  loose  enough  to  be  turned  on  the 
shaft  by  hand.  The  explanation  furnished  for  the 
absence  of  friction  is,  that  the  belt  drawing  the  pulley 
always  in  the  same  direction,  accompanied  by  rotation 
of  both  shaft  and  pulley,  any  change  of  load  permits 
of  the  pulley  assuming  an  appropriate  angular  position 
with  respect  to  the  shaft  by  rolling  on  the  shaft ;  con- 
sequently, in  the  standardizing  and  operation  of  these 
dynamometers  centrifugal  force  and  friction  are  neg- 
lected because  they  can  exert  no  appreciable  influence; 
the  actual  resistance  which  the  springs  offer  for  various 
degrees  of  elongation  being  the  one  thing  which  is 
taken  into  account  in  calibrating  any  scale. 

Different  sizes  of  these  dynamometers  have  been 
employed  in  the  measurement  of  power  required  by 
mills,  tenants,  and  machines,  requiring  from  a  fraction 
of  a  horse-power  up  to  several  hundred  horse-powers, 
and  under  the  widest  range  of  circumstances. 

The  facility  with  which  they  may  be  applied,  and 
their  precision  in  indication  of  the  lighest  to  the  heavi- 


136 


DYNAMOMETERS 


est  loads,  have  earned  for  them  a  prominent  place 
among  dynamometers  manufactured  for  general  use. 

Two  Van  Winkle  dynamometers  furnished  to  a 
firm  in  Antofagasta,  Chili,  respectively  of  450  and 
of  600  horse-power  capacity,  at  120  revolutions  per 
minute  transmit  the  power  of  two  9-inch  shafts. 
They  are  believed  to  be  the  most  powerful  rotary 
transmitting-dynamometers,  of  any  type,  ever  con- 
structed. 

While  investigating  the  subject  of  power  transmis- 
sion as  applied  to  milling-machines,  the  writer  con- 
structed an  apparatus  shown  in  Fig.  59  by  which  he 


FIG.  59. 


proposed  to  measure  the  magnitude  of  the  force  exerted 
by  the  teeth  of  the  cutter,  but  the  results  were  not 
wholly  satisfactory  when  applied  to  a  milling-machine. 
Used  on  a  planer,  however,  a  measure  of  the  useful 


AND    THE  MEASUREMENT  OF  POWER.         \tf 

work  was  readily  obtained  from  the  card  taken  from 
the  indicator  attached. 

Prof.  L.  P.  Breckenridge,  of  the  Michigan  Agricul- 
tural College,  had  previously  made  some  interesting  ex- 
periments with  a  similar  apparatus  for  determining  the 
pressure  exerted  by  a  drill  working  under  similar  con- 
ditions, and  more  recently  has  successfully  applied  the 
apparatus  to  planer  tools.  (See  American  Machinist, 
August  14,  1890.)  The  action  will  be  understood  by 
an  inspection  of  the  figure.  The  thrust  of  the  tool 
acts  upon  the  planger  of  the  cylinder,  thereby  forcing 
the  contained  oil  into  the  pressure-gauge  and  into  the 
cylinder  of  the  indicator.  By  a  suitable  arrangement 
of  cords,  the  drum  of  the  indicator  is  made  to  revolve 
synchronously  with  the  stroke  of  the  tool  or  with  the 
work;  and  as  the  pencil  is  forced  upwards  by  the 
pressure  exerted  at  the  point  of  the  tool,  it  will  be 
seen  that  a  measure  of  the  work  performed  can  be  ob- 
tained from  the  card.  The  gauge  is  simply  a  check  on 
the  indicator.  It  is  evident  that  the  total  work  per- 
formed cannot  be  obtained  by  this  means,  as  the  force 
required  to  drive  the  machine  itself  is  disregarded. 

To  obtain  the  total  work,  and  at  the  same  time  the 
useful  effect,  the  writer  next  designed  the  hydraulic 
dynamometer  shown  in  Figs.  60  to  62.  The  plan  of 
mounting  the  cylinder  upon  a  rotating  pulley  was  ob- 
tained from  an  article  which  appeared  in  Industries* 
but  the  details  and  arrangement  of  the  present  dyna- 
mometer are  in  many  respects  very  different  from  the 
one  there  illustrated.  To  maintain  the  lever-arm  con- 

*  See  also  Sc.  American  Sup.,  Feb.  g,  1889. 


138  DYNAMOMETERS 


FIG.  6o.-FLATHER  HYDRAULIC  DYNAMOMETER. 


AND    THE  MEASUREMENT  OF  POWER.         139 

slant,  the  cylinder  through  which  the  transmitting 
force  acts  should  not  be  bolted  rigidly  to  the  pulley- 
arm,  as  in  the  case  with  the  machine  just  referred  to, 
but  should  be  pivoted  in  such  a  manner  as  to  obtain 
a  constant  lever-arm.  The  action  of  the  Flather  dyna- 
mometer is  this: 

The  pulley  L,  which  receives  the  power,  is  loose  on  the 
shaft  and  free  to  turn  within  certain  limits.  F,  secured 
to  the  shaft,  is  belted  to  the  machine  to  be  tested,  and 
carries  a  cylinder,  C,  which  is  supported  on  trunnions 
by  means  of  the  brackets  b ;  this  cylinder  is  partially 
filled  with  oil,  and  connected  to  centre  of  shaft  by  a 
small  flexible  tube.  The  end  of  the  shaft  is  bored 
out  and  is  provided  with  a  hollow  steel  tube  free  to 
revolve  in  the  spindle  and  fitted  with  gland  and  stuff- 
ing-box nut  to  prevent  leakage  of  oil.  Connected  with 
this  steel  tube  is  the  stand  S,  carrying  a  pressure- 
gauge  and  an  indicator.  When  motion  is  given  to 
the  pulley  L  it  revolves  through  a  small  arc  until  a 
steel  pin  in  its  arm  comes  in  contact  with  the  plunger 
in  cylinder  C.  If  there  is  no  resistance  to  be  over- 
come, the  indicator-pencil  and  gauge  finger  remain 
at  zero ;  but  as  soon  as  resistance  occurs  the  plunger 
is  forced  inwards.  When  the  power  overcomes  the 
resistance,  motion  is  communicated  to  the  pulley  F, 
and  the  machine  is  driven  through  the  force  trans- 
mitted by  the  oil. 

As  the  plunger  is  forced  inwards,  the  indicator- 
pencil  and  gauge-finger  will  in  consequence  rise,  and 
the  amount  of  rise  will  determine  the  pressure  per 
square  inch  acting  on  the  plunger.  If  the  distance  of 
the  lever-arm  acting  on  the  plunger  is  known,  the 


140 


D  YNAMOME  TEKS 


U  LJ 


FIG.  61. 


AND    THE  MEASUREMENT  OF  POWER.         141 


1 42  D  YNAMOME  TERS. 

power  can  be  readily  ascertained  from  the  formula 
P  X  2nrN 


H.P.= 


12  X  33000 


in  which  r  equals  radius  in  inches  of  path  traversed, 
and  .A^  equals  number  of  revolutions  per  minute.  If 
the  construction  of  the  machine  be  such  that  r  is  con- 
stant, as  in  the  present  case,  and  equal  to  C,  the 
formula  becomes  : 


o.o  oo  i 
H.P.  =  -     ~-~     -  =  o.oo  ooi  586/>AT. 


When  r  is  variable  its  exact  determination  would  be  a 
difficult  matter,  but  if  this  variation  of  arm  be  neg- 
lected the  final  result  will  be  vitiated. 

In  the  experimental  machine  constructed  by  the 
writer  the  pulleys  were  each  12  inches  in  diameter  and 
3^  inches  face  ;  the  cylinders  were  1.954  inches  in  diam- 
eter, presenting  an  area  of  3  square  inches.  The 
plungers  were  of  hard  bronze  and  were  kept  tight  by 
leather  cup-washers  secured  to  the  end  ;  grooves  in 
the  plunger,  as  for  water-packing,  and  cast-iron  piston- 
rings  were  successively  used,  but  abandoned  after  a 
short  trial  as  not  being  trustworthy.  A  5-lb.  spring 
was  used  in  the  indicator  (a  Tabor),  as  with  stronger 
springs  the  card  obtained  was  not  sufficiently  large  to 
show  the  delicate  changes  which  it  was  desired  to  bring 
out.  Instead  of  a  piston  having  an  area  of  3  square 
inches,  the  results  of  experiments  show  that  an  area  of 
2  or  even  I  inch  would  have  been  more  satisfactory 
for  the  work  in  hand. 


1  44  D  YNA  MOME  TERS 

It  would  seem  that  the  centrifugal  force  of  the 
plunger  would  materially  affect  the  true  value  of  the 
force  transmitted,  but  a  careful  examination  of  this 
force  with  varying  lever-arms,  corresponding  to  different 
positions  of  the  plunger,  shows  that  the  actual  effect 
is  very  small. 

As  the  lever-arm  of  the  driving  force  is  constant, 
the  centre  of  gravity  of  the  plunger  will  have  a  vary- 
ing arm  dependent  upon  its  position  relative  to  the 
cylinder.  This  is  shown  in  Fig.  63,  in  which  G,  G',  and 
G"  are  three  positions  of  the  centre  of  the  plunger, 
the  lever-arms  of  which  are  3.67  inches,  3.87  inches, 
and  3.50  inches  respectively  —  the  radius  of  the  driving 
force  being  constant  and  equal  to  3.6  inches. 

The  centrifugal  force,/,  of  the  plunger  can  be  calcu- 
lated from  the  formula 


W  being  the  weight  in  pounds,  r  the  radius  in  inches, 
and  N  the  number  of  revolutions  per  minute.  In  the 
case  before  us  IV=  1.75  pounds.  If  we  assume  A^to 
equal  100,  150,  200,  250,  we  obtain  for/  the  values 
shown  in  the  following  diagrams,  Figs.  64,  65,  66. 

As  the  centrifugal  force  acts  along  the  radial  line 
through  the  centre  of  gravity  of  the  plunger,  it  will  be 
seen  that  only  the  horizontal  component  can  be  con- 
sidered as  a  force  acting  in  the  direction  of  motion. 
If  we  assume  the  average  radius  of  the  centre  of  gravity 
of  the  plunger  (3.67  inches),  and  the  average  number 
of  revolutions  per  minute  to  be  175  we  find  from  Fig. 
64  that  the  corresponding  value  of  /  is  5.7  pounds,  as 


AND    THE  MEASUREMENT  OF  POWER.         145 


c      I  igfcsss^^NSsss  \  *£*%:  ^s^S^ww 

^    I  •:! 


G  is  center  of  gravity  for  mean  position,. 

G  "       "       "        "         "    inner         »       ,  \\ 

G""       "       "         "          "    outer          '*  \    \J 


FIG.  63. 


i46 


DYNAMOMETERS 


shown  by  dotted  coordinates.  If  \ve  decompose  this 
force  into  its  two  components  (see  Fig.  63),  we  find  the 
horizontal  component  is  1.37  pounds,  the  vertical  being 
5  pounds ;  now  the  vertical  component  produces  a  cer- 
tain amount  of  friction  against  the  walls  of  the  cylinder 
which  retards  the  motion  of  the  plunger  ;  if  we  take 
the  coefficient  of  friction  in  this  case  to  equal  seven 


FIG.  64. 


?.-,o 

^ 

<- 

^~ 

3  ro 

- 

- 

*r 

s_ 

/ 

/ 

-.  10° 
{ 

t* 

/ 

\ 

/ 

0 

1  1 

2  £6*. 

FIG.  65. 


,x 

^ 

c 

X 

^^ 

c 

,x" 

/ 

1 

/•I 

/ 

/ 

1234 

5 

J  10  ri  12  w 

per  cent,  we  obtain  0.35  pound  for  the  friction  which 
acts  in  the  opposite  direction  to  that  of  motion,  hence 
1.37  —  .35  =  i. 02  pounds  equals  the  effective  compo- 
nent of  the  centrifugal  force.  As  this  acts  on  an  area 
of  3  square  inches,  the  effective  component  at  the  given 
speed  is  only  0.34  pound  per  square  inch,  which,  if 


AND    THE  MEASUREMENT  OF  POWER.         147 

there  were  no  friction  in  the  machine,  would  have  to 
be  deducted  from  the  actual  force  as  indicated  on  the 
pressure-gauge  or  card. 

Experiments  to  ascertain  the  friction  of  the  machine 
showed  that  0.425  foot-pound,  only,  was  necessary  to 
overcome  the  friction  when  the  machine  was  at  rest 
with  belts  thrown  off.  With  the  sensitive  spring  used 
in  the  indicator  very  small  changes  in  the  forces  were 
determinable.  At  the  ordinary  speeds  at  which  the 
machine  was  run  there  was  no  appreciable  difference 
in  pressure,  as  shown  by  the  zero  line,  whether  tlu 
machine  was  stopped  or  running  with  the  transmitting 
belt  thrown  off ;  with  both  belts  on,  however,  a  resist- 
ance at  the  plunger  as  small  as  three-fourths  pound 
could  readily  be  determined,  as  will  be  shown  subse- 
quently. From  this  it  was  concluded  that  for  ordinary 
speeds  the  effect  of  the  centrifugal  force  of  the  plunger 
was  neutralized  by  the  friction  in  the  dynamometer;  in 
any  case  it  could  be  neglected  by  obtaining  the  zero 
line  when  running  free  at  a  given  speed. 

The  small  coiled  spring  outside  of  the  cylinder,  Fig. 
61,  connecting  the  arms  of  the  loose  pulley  L  with  the 
bracket  b,  keeps  the  pin/  in  contact  with  the  plunger; 
the  action  of  this  spring  is  to  force  the  plunger  into 
the  cylinder,  and  thus  raise  the  pressure  on  the  gauge  ; 
this  force  is,  however,  counteracted  by  another  spring 
inside  the  cylinder,  which  resists  the  inward  motion  of 
the  plunger,  yet  acts  with  an  equal  force  to  keep  the 
plunger  in  contact  with  the  pin.  When  resistance  is 
applied  to  the  pulley  jpthe  plunger  is  forced  into  the 
cylinder  until  this  resistance  is  overcome;  the  inner 
spring  is  thereby  compressed  and  presents  a  resistance 


I 48  D  YNAMOME  TERS 

to  the  motion  of  the  piston.  As  the  spring  is  very 
light,  and  the  compression  seldom  exceeds  half  an  inch, 
it  will  be  seen  that  this  force  of  resistance  is  hardly 
appreciable. 

An  examination  of  an  indicator-card,  Fig.  67,  from 


SCAUE,..5»«  
Ft.P.M,..Za«A«36  Dyn.l4Hg  1 

1 
•1 

Cut-  V'             ^/  \        METAL(—  Wrought  Iran. 

F  S  E  D._  .48  per  inch.           •!  *  ,T 

j= 

\     roO(.r..O;amoii(J  point. 
f!ov,r  feed  H./ht 

—  ^  —  btsufi-,  f  (  9*.  t.ty.ir.s  i/i. 

this  dynamometer  shows  that  the  power  required  to 
drive  a  i6-inch  Flather  lathe  with  back  gears  in,  well 
lubricated,  and  running  light  at  36  revolutions  per 
minute,  is 

PV 


o.i  i  X  (5  X  3  G")  X  211  X  3.6"  X  140 

--  =°.o'  3 


=  434-3  foot-pounds, 

where  o.u  equals  the  height  of  card  in  inches;  5 
pounds  equals  the  spring  used  ;  area  of  cylinder-piston 
equals  3  inches  ;  radius  of  arm  equals  3.6  inches  ;  the 
revolutions  of  dynamometer  being  140  per  minute. 
With  the  screw  feed  in,  still  running  light,  the  power 


AND    THE  MEASUREMENT  OF  POWER.         149 

was  found  to  be  0.020  H.  P.,  or  710.6  foot-pounds; 
with  the  load  on,  which  was  a  light  cut  T*g-  inch  deep 
on  a  round  bar  of  wrought-iron  with  diamond-pointed 
tool,  the  maximum  power  registered  was  0.102  H.  P., 
or  3474  foot-pounds. 


SOALE....5/6*  MACHWEj 

R.P.M^ Lathe  36  DynJjD  METAL,, 

»       210     "      « 


FEEOj....  4^per  twci  TOOL,, 

Work  of  Machine. 


FIG.  68. — FRICTION-CARD  FOR  i6-iNCH  LATHE. 

A  peculiar  result,  shown  in  Fig.  68,  was  obtained  on 
several  cards,  this  being  a  greater  amount  of  power 
used  to  drive  the  lathe  running  free  without  back- 
gears  than  under  the  same  conditions  with  the  back- 
gears  thrown  in. 

A  somewhat  similar  occurrence,  repeatedly  con- 
firmed, was  noticed  by  Mr.  Wilfred  Lewis  in  the 
course  of  some  experiments  with  a  48-inch  lathe. 

The  probable  reason  for  this  is  that  the  work  of 
friction  in  the  spindle-brasses  and  other  bearings  is 
much  less  at  the  lower  velocity.  With  the  belt  on 
any  given  step  of  a  four-stepped  cone-pulley  the 
reduction  of  velocity  in  the  main  spindle-journals, 
when  back-gears  are  thrown  in,  will  be  about  nine 
to  one,  which  reduces  the  work  of  friction  very 


1 50  D  YXA  MOMK  TERS 

materially ;  the  superior  lubrication  of  the  cone-pul- 
ley due  to  the  revolving  spindle  also  reduces  its  fric- 
tion below  that  required  to  drive  the  spindle  at  the 
greater  velocity  without  the  back-gears,  and,  with  the 
ratio  of  speeds  as  great  as  that  ordinarily  employed, 
this  reduction  in  journal-friction  more  than  compen- 
sates for  the  work  spent  in  overcoming  the  resistance 
due  to  the  gearing. 


AND    THE  MEASUREMENT  OF  POWER. 


CHAPTER   V. 

POWER   REQUIRED   TO    DRIVE    LATHES. 

It  has  been  stated  that  the  power  required  to  run  a 
small  lathe  while  taking  a  light  cut  in  wrought-iron 
was  one-tenth  horse-power. 

By  a  comparison  of  data  on  the  subject  it  will  be 
seen  that  the  actual  power  consumed  is  quite  variable, 
and  that  the  power  required  to  turn  off  metal  may  be 
much  less  than  that  required  to  file  or  polish  the  same 
in  the  lathe,  or  even  to  run  the  lathe  empty. 

It  is  evident  that  the  power  required  to  do  useful 
work  varies  with  the  depth  and  breadth  of  chip,  with 
the  shape  of  tool,  and  with  the  nature  and  density  of 
metal  operated  upon  ;  and  while  it  would  also  appear 
that  the  power  required  to  run  a  machine  empty  should 
be  constant  for  a  given  speed,  a  little  investigation  will 
show  that  this  latter  is  often  a  variable  quantity. 

In  the  case  of  a  lathe,  for  instance,  when  the  ma- 
chine is  new,  the  working  parts  have  not  become  worn 
or  fitted  to  each  other  as  they  will  be  after  running  a 
few  months;  and  at  first,  the  length  of  time  depending 
on  the  frequency  of  its  use,  the  lathe  will  run  hard, 
in  which  condition  the  power  required  will  be  greater 
than  will  be  the  case  after  the  running  parts  have  be- 
come worn. 


i$2  DYNAMOMETERS 

Another  cause  of  variation  in  this  portion  of  the 
power  absorbed  will  be  found  in  the  driving  belt :  a 
tight  belt  will  increase  the  friction  very  considerably. 
Hence  to  obtain  the  greatest  efficiency  of  a  machine, 
that  is,  the  ratio  of  useful  work  to  total  power  ab- 
sorbed, we  should  use  wide  belts,  and  run  them  just 
tight  enough  to  prevent  slip.  The  belts  should  also 
be  soft  and  pliable,  otherwise  power  is  consumed  in 
bending  them  to  the  curvature  of  the  pulleys. 

Another  point  in  this  connection,  sometimes  over- 
looked, is  the  relative  diameter  of  cone-pulleys.  A 
belt  may  be  wide  enough  and  loose  enough  to  run  well 
on  the  larger  steps  of  the  driven  shaft,  but  on  the 
higher  speeds  may  be  altogether  too  tight.  The  writer 
has  in  mind  a  small  lathe  in  which  it  was  necessary  to 
let  out  the  belt  three  quarters  of  an  inch  when  chang- 
ing from  the  largest  to  the  smallest  step  on  the  cone- 
pulley. 

A  third  cause  is  the  variation  of  journal-friction,  due 
to  slacking  up  or  tightening  the  cap-screws,  and  also 
the  end-thrust  bearing  screw.  When  one  man  runs  a 
lathe  so  that  a  pull  on  the  belt  will  revolve  the  spindle 
half  a  dozen  times,  and  another  man  screws  down  the 
boxes  of  the  same  lathe  so  that  he  can  only  move  the 
spindle  by  a  series  of-  tugs  with  both  hands  on  the  belt, 
no  dynamometer  is  needed  to  show  that  the  power 
absorbed  will  be  different  in  the  two  cases. 

The  power  necessary  to  drive  the  lathe  over  and 
above  that  required  to  turn  off  metal  or  do  useful 
work  is  often  increased  by  setting  up  the  tail-stock 
centre  too  hard,  or  by  letting  the  centre  run  dry. 
In  one  of  the  writer's  experiments  it  was  noticed  that 


AND    THE  MEASUREMENT  OF  POWER.        153 

the  power  absorbed  constantly  increased,  and  with  no 
perceptible  change  in  thickness  of  chip  or  condition 
of  tool.  The  cut  was  smooth  and  clean,  yet  the  dyna- 
mometer showed  nearly  three  times  the  power  ordi- 
narily required.  The  tool  was  withdrawn  from  cut 
with  very  little  change  in  the  pressure ;  a  drop  of  oil 
on  the  dead-centre,  however,  instantly  caused  the  line 
to  fall,  but  the  normal  pressure  was  reached  only 
when  the  centre  was  eased  a  little.  Subsequent  trials 
showed  conclusively  that  the  ordinary  running  power 
could  be  more  than  doubled  by  carelessness  at  this 
point. 

Hartig's*  investigations  show  that  it  requires  less 
total  power  to  turn  off  a  given  weight  of  metal  in  a 
given  time  than  it  does  to  plane  off  the  same  amount  ; 
and  also  that  the  power  is  less  for  large  than  for  small 
diameters.  This  latter  fact  is  readily  understood  when 
we  consider  that  the  faster  we  run  a  lathe-spindle  the 
more  power  it  requires,  provided  we  do  not  consider 
the  intervention  of  intermediate  gear-shafts ;  when 
back  gears  are  used,  the  power  will  be  less  with  the 
belt  running  upon  a  given  step  of  the  cone-pulley  than 
if  the  gears  were  thrown  out,  although  such  power  may 
be  greater  than  that  required  to  produce  a  greater 
number  of  revolutions  of  the  spindle  when  running 
without  back  gears. 

This  is  clearly  shown  in  Table  V,  which  gives  the 
actual  (measured)  horse-power  required  to  drive  a  lathe 
empty  at  varying  numbers  of  revolutions  of  main 
spindle. 

*  Versuche  tiber  Leistung  und  Arbeiis-Verbrauch  der  Werkzeug- 
maschinen. 


'54 


DYNAMOMETERS 


TABLE   V. 
HORSE-POWER  FOR  SMALL  LATHES. 


Without  Back  Gears. 

With  Back  Gears. 

Revolutions 
of  Spindle 
per  minute. 

Horse-power 
required  to 
drive 
empty. 

Revolutions 
of  Spindle 
per  minute. 

Horse-power 
required  to 
drive 
empty. 

Remarks. 

47.0 
80.5 

O.IOI 

.118 

29.0 
49-7 

O.II3 
.128 

12"  lathe  built  by  Zim- 
mermann,  of  Chem- 

138.0 

•M7 

85.3 

•177 

nitz,  Germany. 

47-4 
80.4 
125.0 
188.0 

•159 
.202 
•259 
•339 

4-84 
8.18 

12.8 

19.2 

.132 
.150 
.187 
•  230 

Small  lathe  (i3i")  built 
by       Zimmermann. 
New  machine. 

54-6 
82.2 

122.0 
183.0 

.206 
.260 

•339 

•455 

6.61 

9-95 
14.8 

22.  I 

•157 
•177 
.206 

•249 

\1\"    lathe    built     by 
Zimmermann.    New 
machine. 

81.11 

.126 

8-34 

*.I33 

132.72 

219.08 

•MS 
.197 

14.6 

24-33 

'14?         20"  Fitchburg  lathe. 

365.00 

.310             38.42 

•  274 

iS.8 

.086 

2.31 

•  035 

33-5 

•137 

4.12 

.047 

26"  lathe  built  by  Zim- 

54-6 

.210 

6.72 

•  063 

mermann. 

82.2 

.326      |       10.8 

.087 

*  Horse-power  greater  than  should  be  the  case,  on  account  of  belt  rubbing  on 
back-gear  hollow  shaft. 

The  only  exception  is  the  series  of  values  given  for 
the  12-inch  lathe,  which  show  a  larger  horse-power  when 
the  back  gears  are  thrown  in. 

It  will  be  noticed  that  the  relative  speeds  of  the 
spindle  in  this  lathe  are  not  properly  proportioned, 
there  being,  practically,  only  four  variations  of  speed, 
whereas  there  should  be  six. 


AXD   THE- MEASUREMENT  OF  POWER.        155 

The  ratio  of  the  smallest  number  of  turns  of  the 
cone  to  the  smallest  number  of  turns  of  the  spindle  is 
||,  or  1.62  to  i,  instead  of  8  or  9  to  i  as  in  the  other 
cases,  from  which  fact  we  are  led  to  conclude  that  if 
the  ratio  be  small  between  the  speed  of  the  cone 
(which  revolves  freely  on  the  spindle  when  back  gears 
are  used)  and  the  speed  of  the  spindle,  the  work  spent 
in  driving  the  spindle  through  the  back  gears  will  be 
greater  than  the  work  saved  by  reduced  friction  in  the 
bearings. 

From  this  it  is  apparent  that  there  will  be  a  certain 
ratio  of  reduction  for  which  the  power  required  to  run 
the  lathe  with  or  without  back  gears  will  be  the  same : 
with  a  greater  ratio  it  will  take  less  power  with  the 
back  gears  in,  and  with  a  lesser  ratio  more  power  will 
be  required. 

Assuming  the  lathe  to  be  in  good  condition,  the 
brasses  a  good  running  fit,  and  the  belt  not  too  tight, 
we  see  from  these  results  that,  in  order  to  estimate  the 
total  horse-power  required  to  do  a  certain  amount  of 
work,  we  must  know  something  about  the  speed  at 
which  the  lathe  will  be  run,  which  speed  is.  of  course, 
dependent  upon  the  diameter  and  nature  of  work. 

If  we  plot  the  curve  of  horse-power  and  revolutions 
from  the  above  table,  we  shall  obtain  straight  lines,  or 
approximately  straight  lines,  as  shown  in  Fig.  69,  which 
is  drawn  for  four  different  lathes  varying  in  size  from  12 
to  20  inches  swing — the  power  necessary  to  drive  with 
back  gears  in  not  being  considered  in  this  diagram. 

Here  the  number  of  revolutions  of  spindle  per 
minute  is  given  on  the  extreme  left,  and  the  horse- 
power on  the  lower  line.  All  the  lines  emanate  near 


ISO  D  YNA  MOME  TERS. 

the  point  A,  and  diverge  with  different  degrees  of 
rapidity.  The  lines  for  the  12-and  2O-inch  lathes  are 
parallel  for  a  portion  of  their  length,  and  show  the 
least  increase  in  horse-power  for  a  given  increase  in 
speed.  The  line  for  the  i/^-inch  lathe  falls  away  very 


0       .05    -4.10.15    AM  .25    .30    .35    .40    .45     .5 


FIG.  69. — HORSE-POWER  REQUIRED  TO  DRIVE  SMALL  LATHES. 

quickly,  which  shows  a  rapid  increase  in  power  for  a 
given  increase  in  number  of  revolutions.  The  average 
for  the  four  lathes  represented  is  given  in  the  line  AB, 
which  strikes  the  base-line  for  horse-power  at  the  point 
about  .095,  corresponding  to  which  the  revolutions  per 
minute  =  o. 

If  we  wish  to  find  the  horse-power  for  any  given 
speed,  say  80  revolutions  per  minute,  we  have  simply 


AND    THE  ^MEASUREMENT  OF  POWER.         157 

to  draw  a  line  parallel  to  the  base  line  from  the  point 
Soon  the  revolution  scale,  until  it  cuts  the  line  AB; 
the  distance  cut  off,  DC,  or  what  is  the  same  thing,  oE, 
will  give  the  horse-power  direct.  In  the  assumed  case 
it  is  .19  +.  As  AB  was  chosen  as  the  mean  of  all  the 
lines  represented,  the  horse  power  measured  upon  it 
can  only  approximate  the  actual,  which,  in  the  extreme 
cases,  12-  and  17^-inch  lathes,  will  vary  more  and  more 
as  the  speed  increases.  If  we  let  //./*.„  =  horse-power 
necessary  to  drive  lathe  empty,  and  N  =.  number  of 
revolutions  per  minute,  then  the  equation  for  the  line 
AB  will  be 

'  H.P.t  =  O.O95  -f  O.OOI2.W. 

In  the  same  way  we  can  plot  similar  curves  for  the 
power  necessary  to  drive  the  lathes  empty  when  the 
back  gears  are  in  ;  from  this  we  can  assume  an  average 
and  find  the  equation  of  the  line  as  before.  With  the 
same  notation  previously  given,  this  equation  for  lathes 
under  20  inches  swing  is 

H. P.,  =  0.10 -\-o.oo6N. 

The  larger  lathes  vary  so  much  in  construction  and 
detail  that  no  general  rule  can  be  obtained  which  will 
give,  even  approximately,  the  power  required  to  run 
them,  and  although  the  formulas  just  obtained  show 
that  at  least  0.095  horse-power  is  needed  to  start  the 
small  lathes,  for  which  the  line  AB  has  been  drawn, 
Fig.  69,  there  are  unquestionably  many  American 
lathes  under  20  inches  swing  working  on  a  consumption 
of  less  than  .05  horse-power. 

The  amount  of  power  required  to  remove  metal  in  a 


158  D  YNAMOME  TERS 

machine  is  also  variable,  but  determinable  within  more 
accurate  limits.  The  shape  and  condition  of  tool,  the 
hardness  of  material  to  be  cut,  the  rate  of  feed  and 
depth  of  cut,  all  affect  the  final  result. 

Every  machinist  has  some  special  form  of  lathe-tool, 
ground  to  some  particular  angle,  and  with  a  given 
amount  of  rake — not  measured,  but  ground  so  it  will 
look  right — which  will  give  the  cleanest  cut,  and  turn 
off  the  metal  quicker  than  any  other  tool  in  the  shop. 

One  man  uses  a  round-nose  tool  with  no  top-rake  for 
cast-iron,  and  with  a  coarse  feed  and  square  chip 
(depth  of  chip  equal  to  the  breadth)  turns  out  con- 
siderable work  during  the  day. 

Another  uses  a  diamond  point,  or  some  other  form, 
which  he  grinds  and  sets  a  little  differently  from  every 
one  else,  and  he,  too,  turns  out  a  large  quantity  of 
work.  For  wrought- iron,  steel,  or  brass,  it  is  the 
same  ;  every  man  has  his  own  form  of  tool  which  he 
considers  will  do  the  best  and  quickest  work. 

Without  entering  into  the  question  of  which  is  the 
better  form  of  tool  to  use  in  a  given  case,  we  shall 
assume  ordinary  conditions,  and  try  to  ascertain  how 
much  power  is  absorbed  by  a  lathe  in  removing  metal ; 
the  power  required  to  run  the  lathe  will  not  be  in- 
cluded in  this  discussion.  As  a  means  of  convenient 
comparison,  the  work  done  has  been  reduced  to  the 
weight  of  metal  removed,  or  that  would  be  removed,  in 
one  hour,  provided  all  conditions  remained  the  same. 

Referring  again  to  Dr.  Hartig's  researches,  we  find, 
in  connection  with  a  13^-inch  lathe,  that  the  greatest 
amount  of  work  done  per  hour  was  11.55  pounds  of 
wrought-iron  removed  under  the  following  conditions : 


AND    THE   MEASUREMENT  OF  POWER.         159 

Cutting  speed  =  24.6  feet  per  minute  ;  breadth  of  cut 
=  .017  inch;  depth  of  cut  =  .08  inch;  horse-power 
(//./I,)  required  to  turn  off  the  metal  =  .230. 

As  a  result  of  twenty-three  experiments  on  this 
lathe,  we  find  that 

H.I\  =  CW, 

where  C  is  a  constant,  and  W  the  weight  of  chips 
removed  per  hour ; 

C  =  .032  for  wrought-iron,  and 
C=  .025  for  cast-iron. 

The  greatest  amount  of  wrought-iron  removed  per 
hour  on  a  i/^-inch  lathe  was  25  pounds;  the  cutting 
speed  was  15.88  feet  per  minute;  breadth  of  cut  was 
.04  inch,  and  thickness  of  chip  —  .20  inch  ;  horse- 
power required  =  .66. 

The  following  is  the  result  of  forty-one  experiments 
on  this  lathe : 

H.P.,  =  CW, 
where,  as  before,  IV  =  weight  of  chips  per  hour  ; 

C=  .045  for  steel, 
=  .027  for  wrought-iron, 
=  .03  for  cast-iron. 

On  a  26-inch  lathe  the  weight  of  chips  removed  per 
hour  =  10.93  pounds ;  the  cutting  speed  —  32  feet  per 
minute  ;  breadth  of  cut  =  .024  inch,  and  thickness  of 
cut  .08  inch  ;  horse-power  required  =  .413.  From  ten 
measurements  the  constant  C  was  found  to  be  .04 
for  cast-iron  ;  as  this  is  25  per  cent  higher  than  ordi- 


1 6O  D  YNAMOME  TERS 

narily  obtained,  we  infer  that  the  iron  was  much  harder, 
or  the  tool  in  poor  condition,  or  perhaps  both  affect 
the  result. 

For  a  heavy  turning  and  facing  lathe  50  inches  swing, 
treble  geared,  as  a  result  of  twenty  experiments,  C 
was  found  to  be  .027  for  cast-iron. 

For  another  heavy  lathe,  56  inches  diameter  of  face- 
plate, C  was  found  to  be  .031  for  cast-iron,  as  a  result 
of  twenty-four  experiments. 

A  small  lathe  of  1 2  inches  swing,  turning  wrought-iron 
at  the  rate  of  4.88  pounds  per  hour,  at  a  velocity  of  23.4 
feet  per  minute,  breadth  of  cut  =  .018  inch,  thickness 
of  chip  =  .062  inch,  required  .21  horse-power.  For 
this  lathe 

C  =  .045  for  wrought-iron, 
=  .028  for  cast-iron. 

From  these  and  other  data  we  find  that  the  horse- 
power required  to  turn  off  metal  can  be  obtained,  if  we 
know  the  amount  of  chips  removed  per  hour,  by  using 
the  formula 

H.P.,  =  CIV, 

in  which  suitable  values  of  C  obtained  from  the  fore- 
going are 

.030  for  cast-iron, 

.032  for  wrought-iron, 

.047  for  steel. 

As  we  should  infer,  the  size  of  lathe,  and  therefore 
the  diameter  of  work,  has  no  apparent  effect  on  the 
cutting  power,  as  shown  by  the  constant  C.  If  the 
lathe  be  heavy  the  cut  can  be  increased,  and  conse- 
quently the  weight  of  chips  increased,  but  the  value  of 


A. YD    THE  MEASUREMENT  OF  POWER. 


161 


C  appears  to  be  about  the  same  for  a  given  metal 
through  several  varying  sizes  of  lathes. 

Mr.  J.  F.  Hobart,  working  on  this  line  a  few  years 
ago,  published  some  interesting  results  in  the  American 
Machinist*  from  which  the  writer  has  computed  the 
average  weight  of  metal  removed  per  hour,  and  the 
corresponding  useful  horse-power — the  horse-power 
required  to  run  lathe  empty  being  neglected, — from 
which  the  values  of  C,  in  the  subjoined  Table  No.  VI, 
have  been  obtained. 

All  the  experiments  were  conducted  on  a  2O-inch 
Fitchburg  lathe  (previously  mentioned  in  Table  V),  and 
the  metal  cut  throughout  was  cast-iron. 

TABLE    VI. 

HORSE-POWKR    REQUIRED    TO    REMOVE    METAL    IN   A    2O-INCH    LATHE. 


t 

3 

1 

-• 

if 

JQ 

u 

S3 

o 

1 

g 

.2 

to! 

JZ 

*0 

'g._j 

J^ 

c 

.2 

.gs 

c 

•o 

^  ^ 

°  w 

a 

1 
g 

H 

Tool  used.                  5  « 

u& 

3 

u 

ii 

K'> 

5s 

3 

1 

2 

|| 

»*-» 

!! 

&| 

11 

"s 

I 

1 

I5 

Is 

4>  3 

_3 

J 

22 

Side  tool                         37  90 

I3-3O 

.025 

2 

T  e 

Diamond                         30  50 

12" 

.  01  5 

.218 

10.  70 

.O2O 

3 

1  3 

17 

Round-nose  42.61 

•125 

.015 

352 

14.95 

.023 

4 

2 

Left  -  hand     round- 

nose    ...        .             26  29 

.    I2S 

.015 

237 

9.22 

.026 

5 

4 

Square  -  faced     tool 

•  *  j/ 

^"  broad  25  82 

•  OT5 

•  I25 

•  255 

9.06 

.028 

6 

I 

Square  -  faced     tool 

^"  broad  25.27 

.048 

.048 

.200 

10.89 

.Ol8 

7 

I 

Square  -  faced     tool 

i"  broad  25.64 

.125 

.015 

.246 

8.99 

.027 

See  American  Machinist,  Sept.  n  and  18,  1886. 


1 62 


D  YNAMOME  TERS 


An  examination  of  the  above  table  shows  that  an 
average  of  .26  horse-power  is  required  to  turn  off  10 
pounds  of  cast-iron  per  hour,  from  which  we  obtain  the 
average  value  of  the  constant  C  =  .024. 

As  will  be  noticed,  most  of  the  cuts  were  taken  so 
that  the  metal  would  be  reduced  \"  in  diameter;  with 
a  broad  surface  cut  and  a  coarse  feed,  as  in  No.  5,  the 
power  required  per  pound  of  chips  removed  in  a  given 
time  was  a  maximum  ;  the  least  power  per  unit  of 
weight  removed  being  required  when  the  chip  was 
square,  as  in  No.  6. 

The  work  of  R.  H.  Smith,*  who  conducted  similar  ex- 
periments in  England  on  a  29-inch  lathe  (i4^-inch  cen- 
tre), has  also  been  cast  into  the  same  form  with  the 
average  results  shown  in  Table  VII. 

TABLE   VII. 
HORSE-POWER  REQUIRED  TO  REMOVE   METAL  IN  A  2g-iNCH  LATHE. 


1 

Cd 

i, 

.a 

i 

IP 

•"I 

£ 

u 

CO 

u  SJ 

U    jj 

.  • 

"o 

Metal. 

in 

o 

«   § 

If 

u 

C 

^ 

ti 

III 

"o 

IS 

•z. 

•s 
u 

1 

>o 

^§.2 

1" 

|3 

4 

Cast-iron  

12.7 

.05 

.046 

.105 

5-49 

.019 

A 

Cast-iron    .    . 

II  .  I 

.135 

.046 

.217 

I  2    06 

.017 

2 

C«ist-iron      .  . 

12.  85 

.04 

.038 

ooS 

i  -  .  yu 

3.66 

.027 

4 

Wrought-iron  

9.6 

•  03 

.046 

.  tiyo 

•059 

2.49 

•  023 

4 

Wrought-iron  

9.1 

.06 

.046 

.138 

4.72 

.029 

4 

Wrought-iron  

7-9 

.14 

.046 

.186 

.019 

2 

Wrought-iron  

9-35 

.045 

.038 

.092 

2-99 

.031 

Steel 

6 

.02 

.046 

I  .03 

.  O42 

4 

Steel  

5.8 

.04 

.046 

.085 

2  .O 

.042 

Steel 

5T 
•  * 

.06 

.108 

2.64 

.O4O 

41 

*See  Cutting  Tools,  by  R.  H.  Smith,  Cassell  &  Co.,  London,  1884. 


AND    THE  MEASUREMENT  OF  POWER.         163 

Besides  the  general  results  which  we  here  obtain, 
the  relative  cutting  speeds  and  amount  of  metal  turned 
off  per  hour  is  quite  significant.  With  the  American 
lathe  the  cutting  speeds  on  cast-iron  were  about  30 
feet  per  minute;  the  German  experiments  on  the  same 
metal  averaged  19  feet,  while  the  English  speeds  on 
cast-iron  were  always  much  less,  varying  from  14  to  2£ 
feet  per  minute. 

The  small  values  of  C,  .017  and  .019,  obtained  for 
cast-iron,  are  probably  due  to  two  reasons :  the  iron 
was  soft  and  of  fine  quality,  known  as  pulley-metal, 
requiring  less  power  to  cut ;  and,  as  Prof.  Smith  re- 
marks, a  lower  cutting  speed  also  takes  less  horse-power. 

In  summing  up  the  results  here  presented,  if  we 
omit  for  the  present  the  power  necessary  to  over- 
come the  internal  friction  of  the  lathe,  there  would 
seem  to  be  no  good  reason  why  an  average  of 
the  cases  cited  should  not  be  taken  as  representing 
average  practice.  Hardness  of  metals  and  forms  of 
tools  vary,  otherwise  the  amount  of  chips  turned  out 
per  hour  per  horse-power  would  be  practically  constant, 
the  higher  cutting  speeds  decreasing  but  slightly  the 
visible  work  done. 

Taking  into  account  these  variations,  we  find  that 
the  weight  of  metal  removed  per  hour,  multiplied  by  a 
certain  constant,  is  equal  to  the  power  necessary  to  do 
the  work. 

This  constant  we  have  deduced  as  follows : 

Cast-iron.  Wrought-iron.    Steel. 

Hartig 0.030  0.032           0.047 

Smith 023  .028             .042 

Hobart 024 

Average    026  .030            .044 


.  1  64  D  YNA  MOME  TEKS 

For  a  cut  under  ordinary  conditions  which  would 
remove  6  pounds  of  cast-iron,  5  pounds  of  wrought-iron, 
or  3^  pounds  of  steel  chips  per  hour,  the  horse-power 
necessary  would  be  practically  the  same. 


CxW=.  026x6    =. 
CxlV—.  030x5    =.i$H.P. 
C  X  W=  .044  X  3i  =  .15  H.P. 

As  previously  shown,  the  power  necessary  to  run 
the  lathe  empty  will  vary  from  about  .05  to  .3  H.P., 
which  should  be  ascertained  and  added  to  the  useful 
horse-power,  to  obtain  the  total  power  expended. 


AND    7^HE   MEASUREMENT  OF  POWER.         10$ 


CHAPTER  VI. 

MEASUREMENT  OF  WATER-POWER. 

IN  testing  a  hydraulic  motor  a  friction-brake  or  other 
absorbing  dynamometer  applied  to  pulley  on  the  driv- 
ing-shaft, as  already  described,  will  give  the  power  de- 
veloped by  the  motor  under  the  given  conditions,  but 
this  power  maybe  less  than  that  which  it  is  possible  to 
attain,  or  which  might  be  developed  by  the  wheel  when 
running  at  a  greater  or  even  a  lesser  speed :  for  if  the 
velocity  of  the  wheel  be  reduced  to  zero,  there  will  be 
no  power  developed ;  and  if,  on  the  other  hand,  the 
speed  be  excessive,  the  water  will  flow  through  the 
motor,  giving  up  but  little  of  its  energy  to  the  wheel. 

In  making  a  test  of  a  hydraulic  motor,  therefore,  it 
will  be  necessary  to  find  the  available  energy  of  the 
water  which  passes  through  the  wheel  in  a  unit  of  time, 
and  also  the  power  developed  by  the  motor  in  the  same 
time  while  running  at  different  velocities  and  with  dif- 
ferent quantities  of  water. 

A  wheel  may  be  working  under  conditions  which 
will  develop  a  maximum  power,  but  the  efficiency  of 
the  motor  may  not  be  so  great  as  when  developing  a 
lesser  power.  The  problem  then  presents  itself  to  de 
termine  the  speed  of  wheel  and  quantity  of  water 
which  will  give  the  maximum  amount  of  power;  and 


1 66  D  YNA  MO  ME  TER  S 

secondly,   to  determine   that    speed    and    quantity  of 
water  which  will  give  the  maximum  efficiency. 

The  efficiency  of  the  motor  in  any  case  will  be  the 
ratio  of  the  useful  work  performed,  as  determined  by  a 
dynamometer,  to  the  theoretical  or  available  work  due 
to  the  energy  of  the  water ;  that  is, 


where 

V  =  efficiency; 

P=  effective  work  of  the  wheel  in  foot-pounds  per 

unit  time ; 

W  =  weight  of  water  passing  the  wheel  per  unit  time ; 
h  =  available  head  of  water  above  the  motor  in  feet. 

If  h  is  the  total  height  of  fall  from  upper  level  in 
head-race  to  lower  level  in  tail-race,  or  if  it  is  the  dif- 
ference in  levels  between  reservoir  and  the  discharge- 
pipe  of  the  motor  when  the  latter  is  supplied  by  a 

P 

system  of  pipes,  we  shall  obtain  in  ij  =  -7777  an  expres- 
sion for  the  efficiency  of  the  fall ;  but  if  h  is  only  the 
height  from  the  level  of  head-race  to  the  motor,  in  the 
one  case,  and  the  effective  pressure-head,  as  determined 
by  a  gauge  in  the  supply-pipe  at  a  point  near  the 
motor,  in  the  other,  then  this  expression  will  give  the 
efficiency  of  the  motor. 

It  will  be  apparent  that  to  obtain  the  greatest  ef- 
ficiency  of  the  fall,  the  wheel  should  be  placed  as  near 
as  possible  to  the  level  of  the  water  in  the  tail-race ; 
and  that  in  the  case  of  motors  supplied  by  systems  of 


AND    THE   MEASUREMENT  OF  POWER.         167 

piping,  the  latter  should  be  arranged  to  reduce  the 
available  head  as  little  as  possible. 

In  determining  the  available  energy  of  a  fall  of 
water,  the  most  important  and  at  the  same  time  most 
difficult  measurement  to  be  made  is  that  of  the  quan- 
tity of  water  delivered  to  the  motor  in  a  given  time. 

If  the  volume  be  small,  the  most  reliable  method  of 
measurement  is  to  weigh  the  water  discharged  into  a 
tank  or  barrel  placed  upon  platform-scales,  as  shown  in 
Fig.  70,  which  represents  an  arrangement  used  at  the 
Lehigh  University  for  testing  a  small  hydraulic  motor. 

For  larger  quantities  the  water  discharged  may  be 
collected  into  a  receiving-tank  of  known  capacity,  and 
its  weight  determined  from  its  volume.  Sometimes 
two  tanks  are  employed,  with  an  automatic  arrange- 
ment by  which  each  tank  is  filled  and  emptied  alter- 
nately. A  counter  attached  to  the  apparatus  gives  the 
number  of  times  each  tank  has  been  filled.  In  ordi- 
nary tests  the  weight  of  a  cubic  foot  of  water  may  be 
assumed  with  sufficient  accuracy  at  62.5  pounds. 

With  the  arrangement  shown  in  Fig.  70  the  quantity 
of  water  passing  the  wheel  per  minute  was  428  pounds 
or  51  gallons  under  a  pressure  at  the  gauge  of  65 
pounds  per  square  inch,  the  diameter  of  nozzle  being 
f  inch. 

The  head  corresponding  to  this  pressure  j<;  150  feet 
(see  page  203)  ;  and  since  the  weight  of  water  passing 
the  wheel  per  minute  is  known,  the  theoretical  horse- 
power may  be  obtained  from 


_.  =  _         = 

33000  33000 


1 68 


D  YNAMOAIE  TERS 


AND    THE  MEASUREMENT  OF  POWER.         169 

With  the  motor  running  at  526  revolutions  per  min- 
ute and  an  unbalanced  pressure  of  6^  pounds  on  the 
scales,  the  lever-arm  of  the  brake  being  1 5  inches,  the 
brake  horse-power  is 

B.H.P.  =  0.0001  904  PRN 

=  o.oooi  904  x  6.25  x  ~l  X  526  =  0.78  ; 

therefore  the  efficiency  under  the  given  condition  was 

0.78 

ri  = =  40  per  cent. 

1-94 

By  lowering  the  pressure  to  30  pounds  per  square 
inch  (equals  69  feet  head),  the  quantity  of  water  pass- 
ing the  wheel  per  minute,  with  the  same  nozzle,  was 
decreased  to  295  pounds,  corresponding  to  which  the 
theoretical  horse-power  is  0.62. 

The  speed  of  wheel  also  being  decreased  to  354 
revolutions  per  minute,  the  brake  horse-power  was 
only  0.40,  but  the  efficiency  has  bee'n  increased  to 

40 

62  =  64  per  cent. 

From  this  it  will  be  seen,  as  previously  noted,  that  a 
wheel  may  develop  a  maximum  horse-power  under 
given  conditions,  but  the  efficiency  may  be  much  less 
than  that  obtained  under  different  conditions  when  the 
horse-power  is  not  so  great.  The  effect  of  varying  the 
size  of  nozzle  with  varying  head  and  load  may  be  seen 
from  the  following  tabulated  results  from  tests  made 


170 


D  YNA  MOME  TERS 


on  a  small  motor  by  Mr.  J.  C.  Escobar,  the  pressure 
ranging  from  30  to  75  pounds  per  square  inch. 

TABLE   VIII. 
TEST  OF  A  SMALL  HYDRAULIC  MOTOR. 


Diameter  of 
Nozzle. 

Gauge  Press- 
ure in  Ibs. 
per  sq.  inch. 

Head  of  Water 
on  Wheel  in 
feet. 

Weight  on 
Scales  in  Ibs. 

4|l 

sa^a 

f||| 

"o 

11. 

Ill 

££  £ 
& 

Theoretic 
Horse-power 
of  Water. 

Effective  or 
Brake  Horse- 
power. 

Efficiency  of 
Wheel,  per 
cent. 

f 

65 

150 

0-5 

428 

668 

1.94 

.OS 

4 

65 

150 

6.25 

428 

526 

I  94 

.7S 

40 

J 

55 

127 

6.0 

391 

404 

1.50 

•57 

38 

*l 

45 

104 

6.0 

346 

341 

1.09 

.48 

44 

35 

81 

5-o 

3io 

341 

0  78 

•41 

52 

30  |   69 

4-75 

295 

354 

0.62 

.40 

64 

75 

173 

0-5 

276 

697 

1-45 

.08 

6 

75 

173 

6.25 

276 

544 

i-45 

.Si 

56 

65 

150 

6.0 

255 

468 

1.25 

.67 

60 

1 

55 

127 

4-5 

238 

571 

0.91 

.61 

66 

45 

104 

4.0 

220 

521 

0.69 

•49 

7i 

35 

81 

3-5 

198 

375 

0.48 

•3i 

63 

I 

30 

69 

3-o 

172 

412 

0.36 

.22 

61 

r 

75 

173 

0-5 

119 

812 

0.62 

.09 

15 

75 

173 

3-5 

119 

428 

0.62 

•35 

57 

H 

65 

150 

3-5 

112 

380 

0.41 

•3i 

75 

55 

127 

3-0 

104 

400 

0.40 

.28 

7i 

I 

45 

104 

2-75 

*> 

334 

0-33 

.22 

65 

The  following  results  will  show  very  clearly  the  effect 
of  varying  the  load  for  the  same  head  and  diameter  of 
nozzle.  It  will  be  noticed  that  as  the  load  increases  the 
speed  decreases,  and  that  the  power  developed  increases 
with  the  load  up  to  a  given  poin*-;  beyond  this,  how- 
ever, the  power,  and  hence  the  efficiency,  decreases  as 
the  load  is  increased. 


AND    THE  MEASUREMENT  OF  POWER.         I/I 

TABLE    IX. 
EFFECT  OF  INCREASING  LOAD  FOR  A  GIVEN  NOZZLE. 


Weight  on 
Scales  in  Ibs. 

Revolutions  of 
Wheel  per 
minute. 

Theoretic 
Horse-power 
of  Water. 

Effective  or 
Brake  Horse- 
power. 

Efficiency  of 
Wheel,  per 
cent. 

0-5 

651 

O.QI2 

0.07 

8 

I.O 

637 

•15 

16 

i-5 

624 

.22 

24 

2.0 

618 

•29 

32 

2.5 

612 

•36 

39 

3-o 

600 

•42 

46 

3-5 

594 

•49 

53 

4.0 

588 

•36 

61 

4-5 

571 

.61 

66 

5-o 

544 

•65 

70 

5-5 

517 

.68 

73 

5-75 

433 

.66 

72 

Gauge  pressure  =  55  pounds,  corresponding  to  a  head  of  127  feet  ; 
diameter  of  nozzle  =  f  inch. 

For  larger  wheels  the  following  methods  for  deter- 
mining the  quantity  of  water  are  employed  :  determi- 
nation of  the  velocity  of  flow  in  a  conduit  of  known 
cross-section  by  means  of  floats  or  current-meters ; 
direct  measurement  by  various  forms  of  water-meter; 
measurement  over  weirs  and  through  orifices. 

When  current-meters  are  used  it  is  customary  to 
divide  a  section  of  the  stream  (taken  at  right  angles  to 
the  general  direction  of  flow)  into  a  number  of  parts, 
preferably  of  equal  area,  and  to  observe  the  velocity,  as 
indicated  by  the  current-meter,  in  each  of  these  parts. 
From  the  mean  of  the  observed  velocities  at  different 
depths  in  each  subdivision  of  the  section  the  average 
velocity  of  the  whole  section  is  obtained  ;  by  multiply- 


1 72  D  YNA  MOME  TERK 

ing  the  area  of  cross-section  by  the  velocity  per  second 
the  quantity  of  water  passing  through  the  section  per 
second  will  be  obtained. 

If    A  —  area  of   channel  at  the   given  section    in 

square  feet ; 
Vm  =  average   velocity   of    current    in    feet    per 

second ; 

Q  =  cubic  feet   of  water  passing  through    the 
channel  per  second, — 

then 

A  Vw  =  Q. 

A  closer  determination  may  be  made  by  ascertaining 
the  discharge  of  each  subdivision  from  its  area  and 
mean  velocity;  the  discharge  of  the  stream  will  then 
be  the  sum  of  the  discharges  thus  found. 

.It  is  evident  that  the  mean  velocity  of  each  sub- 
division, and  hence  of  the  entire  section,  will  be  more 
closely  determined  the  greater  the  number  of  vertical 
stations  across  the  stream. 

A  very  accurate  method  of  obtaining  the  area  at 
the  given  section  in  narrow  streams  or  small  navigable 
rivers  is  to  run  a  cord  or  wire  across  the  channel  at 
right  angles  to  the  stream,  and  to  take  a  number  of 
soundings  at  equal  intervals  measured  along  the  wire. 

The  lead  for  the  soundings  should  be  of  sufficient 
weight  to  insure  a  vertical  measurement  in  every  case; 
its  weight  varies  from  five  pounds  for  shallow,  still 
water  to  twenty  pounds  for  deep  and  swift  currents. 
A  long  cylindrical  shape,  similar  to  a  sash-weight, 


AND    THE  MEASUREMENT  OF  POWER.         1/3 

offering  little  resistance  to  the  water,  is  suitable  for 
the  purpose.* 

It  is  essential  that  the  cord  attached  to  the  lead 
should  be  thoroughly  stretched  before  being  graduated. 
The  graduations  are  placed  one  foot  apart  and  indicated 
by  a  small  strip  of  cotton  attached  to  the  line,  every 
five  feet  being  denoted  by  a  leather  strip. 

Sounding-poles  are  preferable  for  shallow  channels, 
and  should  be  graduated  to  feet  and  tenths. 

When  float-measurements  are  used  to  ascertain  the 
velocity  of  the  current,  it  is  advisable  to  take  sound- 
ings in  two  sections,  in  order  to  determine  accurately 
the  discharge  of  the  stream. 

If  a  sufficient  number  of  soundings  be  made,  and  the 
results  plotted  on  section  paper,  the  free-hand  curve 
joining  the  lower  ends  of  the  vertical  ordinates  will 
represent  very  closely  the  contour  of  the  bed  of  the 
channel,  from  which  the  area  of  the  section  may  be 
obtained,  either  by  the  use  of  a  planimeter  or  by  one 
of  the  approximate  methods. 

For  subsequent  use  in  determining  the  height  of  the 
water,  a  permanent  bench-mark,  as  for  instance  a  spike 
driven  into  a  tree-stump,  should  be  established  in  the 
immediate  vicinity  and  a  water-gauge  located  near  by. 
For  this  purpose  a  white-painted  board,  graduated  to 
feet  and  tenths  plainly  marked  in  black,  is  fastened  to 
a  stake  or  post  firmly  set  at  the  edge  of  the  water; 
the  zero-point  of  the  scale  is  located  with  reference  to 
the  bench-mark  previously  set,  which  also  provides  a 


*  Johnson's  Surveying.     Wiley  &  Sons,  1890. 


1 74  D  YNA  MO  ME  TERS 

means  of  resetting  the  gauge  in  case  of  disturbance  or 
renewal. 

The  current-meter  used  at  the  present  time  is  gen- 
erally some  modification  of  Woltmann's  Mill  or  Tachom- 
eter shown  in  Fig.  71,  which  consists  of  a  small  wheel 
with  inclined  floats  or  vanes,  /%  held  in  the  current, 


FIG.  71.— WOLTMANN'S  MILL. 

which  causes  it  to  revolve  at  a  speed  nearly  propor- 
tional to  the  velocity  of  the  water  passing  it.  By  a 
suitable  arrangement  of  gearing  connection  is  made 
with  an  indicator  which  records  the  number  of  revolu- 
tions. Sometimes  a  rudder  is  attached  to  cause  the 


AND    THE   MEASUREMENT  OF  POWER. 


175 


wheel  to  face  the  current.  The  apparatus  is  either 
held  at  the  extremity  of  a  pole,  D,  or,  by  being  adjust- 
able along  a  vertical  rod  fixed  in  the  bed,  it  may  be 
set  at  any  desired  depth  below  the  surface. 

That  the  exact  number  of  revolutions  in  a  given 
time  may  be  obtained,  the  instrument  is  arranged  with 
a  cord  and  spring  so  that  the  recording  device  may  be 
thrown  in  or  out  of  gear  at  any  instant. 

In  some  of  the  more  recent  instruments  electrical 
connection  is  made  with  the  rotating  shaft  by  a  "  make- 
and-break  contact,"  and  the  number  of  revolutions  are 
shown  on  a  registering  apparatus  on  shore  or  at  the 
surface  of  the  water  in  a  boat,  as  the  case  may  be. 


FIG.  72.— CURRENT-METER. 

The  form  of  current-meter  shown  in  Fig.  72  *  was 
used  upon  the  gauging  of  the  Connecticut  River,  and 
was  designed  particularly  to  avoid  the  catching  of  float- 
ing substances,  such  as  leaves  and  grass,  upon  either 
the  vanes  or  the  axis,  and  to  render  the  record  of  the 
instrument  independent  of  the  position  of  its  axis 
with  respect  to  the  line  of  the  current  :  also  to  get  less 
friction  upon  the  axis,  so  as  to  measure  low  velocities 
accurately. 

*  Made  by  Buff  &  Berger,  Boston. 


1 76  D  YNA  MOME  TERS 

This  current-meter  is  also  adapted  to  be  used  with 
an  electric  register  for  showing  the  number  of  revolu- 
tions of  the  wheel.  It  is  constructed  upon  the  principle 
of  Robinson's  anemometer,  turning  by  the  difference 
of  pressure  upon  opposite  vanes  of  the  wheel.  The 
vanes  of  this  meter,  however,  instead  of  being  hemi- 
spherical cups  with  a  straight  stem,  are  made  conical  at 
the  ends,  and  are  hollow  and  taper  to  the  central  hub, 
so  as  to  offer  no  obstruction  to  the  slipping  off  of  straws, 
leaves,  or  grass  as  the  wheel  revolves.  The  central 
hub  is  made  tapering,  so  that  any  object  can  slide  off 
easily,  and  it  extends  over  the  joints  at  the  ends  of  the 
axis,  so  as  to  enclose  and  protect  them  from  floating 
substances. 

The  axis  runs  in  agates,  through  which  a  fine  plati- 
num wire  connects  with  the  metal  of  the  frame. 

The  forward  end  of  the  frame  which  carries  the 
wheel  can  be  turned  and  secured  in  any  position  so 
that  the  wheel  can  be  horizontal,  vertical,  or  at  any 
desired  angle. 

The  electrical  connection  is  made  by  carrying  an  in- 
sulated wire  from  near  the  centre  of  the  instrument, 
where  the  insulated  wire  from  the  battery  is  attached 
to  it  when  in  use,  out  to  the  end  of  one  arm  of  the 
wheel-frame,  where  it  ends  in  a  fine  platinum  wire 
resting  upon  a  ring  in  the  hub  of  the  wheel.  This 
ring  is  made  of  alternate  interchangeable  sections  of 
silver  and  hard  rubber,  secured  in  place  by  screws,  so 
that  their  position  can  be  changed  to  register  whole  or 
part  revolutions  as  desired. 

There  is  also  a  socket  and  set-screw  in  the  body  of 
the  frame  near  the  centre,  for  the  return-current,  which 


AND    THE  MEASUREMENT  OF  POWER. 


177 


can  be  carried  most  conveniently  through  a  plain  wire 
slightly  twisted  around  the  in- 
sulated wire  so  as  to  form  one 
cord.  If  the  instrument  is  run 
upon  a  wire,  or  has  a  metallic 
connection  with  the  surface,  the 
return-current  can  be  made 
through  that. 

This  meter  can  be  used  in 
connection  with  any  apparatus 
for  registering  the  revolutions 
of  the  wheel  by  the  breaks  in 
the  electric  circuit. 

The  Price  current-meter,* 
which  is  used  to  a  considerable 
extent  by  the  U.  S.  Coast  and 
Geodetic  Survey,  is  shown  in 
Fig-  73- 


Made  by  W.  &  L.  E.  Gurley,  Troy,  N.  Y. 


D  YNAMOAIE  TERS 


The  wheel  of  this  meter  carries  five  conical  buckets, 
very  strongly  and  compactly  formed  so  as  to  be  able 
to  resist  injury  from  floating  driftwood,  while  at  the 
same  time  it  is  so  designed  as  not  to  be  liable  to  ob- 
struction from  leaves  or  grass. 

A  hollow  trunnion  fitting  freely  upon  the  rod  sup- 
ports the  frame  by  a  pivot  on  each  side,  and  thus  by 
the  rod  and  pivots  the  meter  is  free  to  move  both 
horizontally  and  vertically,  and  so  adjust  itself  to  the 
direction  of  the  current. 

The  rod  is  of  brass,  f  inch   in  diameter  and   2  feet 
long,  its  upper  end  having  an  eye   of  brass  screwed 
firmly  on  and  pinned,  and  its  lower  end  screwed  into  a 
brass  socket  in   the  weight  B,  and  secured  by  a  nut. 
The  weight  B  is  of  lead  and  weighs 
ELECTRIC  REGISTER  about    sixty    pounds ;     it    has    a 

rudder  of  wood,  which  can  be  set 
at  any  angle  with  the  weight,  or 
turned  up  parallel  with  the  rod 
when  not  in  use.  This  weight  is 
only  used  for  deep-water  and 
harbor  surveying  where  the  cur- 
rents are  very  strong.  For  shal- 
FIG.  74.  lower  waters  the  meter  is  used 

upon  a  rod  of  wood  or  metal. 

The  electric  register  used  with  this  instrument  is 
shown  in  Fig.  74. 

Before  using  a  current-meter  it  will  be  necessary  to 
calibrate  it  in  order  to  ascertain  the  number  of  revolu- 
tions of  the  wheel  with  known  velocities  of  current. 
The  calibration  of  the  instrument  is  most  readily  ob- 
tained by  causing  it  to  pass  through  a  measured  dis- 


AND    THE  MEASUREMENT  OF  POWER.         1/9 

tance  at  a  uniform  velocity  in  still  water  not  less  than 
5  feet  deep.  To  secure  a  good  rating  there  should  be 
no  wind  and  the  meter  should  be  immersed  to  a  depth 
of  about  2  feet  below  the  surface.  The  usual  method 
of  obtaining  the  velocities  for  rating  the  meter  is  to 
attach  the  instrument  to  a  vertical  rod  which  projects 
2  or  3  feet  in  front  of  the  bow  of  a  small  boat,  and  to 
either  row  or  pull  the  boat,  by  means  of  cords,  at  as 
uniform  a  rate  as  possible,  over  a  measured  course  of 
about  200  feet,  observers  on  shore  noting  the  exact 
time  of  passing  the  range-lines.  By  varying  the  speed 
of  the  boat  for  successive  passages,  which  should  be  at 
a  uniform  rate,  a  table  of  constants  may  be  computed 
from  which  the  velocity  of  any  current  can  be  deter- 
mined  from  the  number  of  revolutions  per  minute  as 
shown  on  the  dial. 

Frequent  ratings  of  a  meter  while  in  use  will  insure 
reliability  in  its  readings. 

In  the  method  of  measurement  by  surface-floats  the 
velocity  is  obtained  by  observing  the  time  of  transit 
of  a  light  floating  body,  such  as  a  flat  disk,  or  ball  of 
wood,  over  a  known  distance.  By  placing  several  floats 
across  a  stream  and  noting  their  velocities,  the  average 
surface-velocity  may  be  approximately  computed,  but 
this  method  is  apt  to  be  very  inaccurate  when  there 
are  any  local  disturbances  due  to  wind  or  eddies  in  the 
current.  The  use  of  double  floats  presents  a  much 
more  reliable  means  of  obtaining  the  velocity. 

As  in  the  method  with  current-meters  the  velocity 
of  the  filaments  should  be  ascertained  in  several  verti- 
cals across  the  stream  and  at  various  depths  below  the 
surface.  For  this  purpose  a  body  slightly  heavier  than 


1 8O  D  YNA  MO  ME  TERS 

the  water  is  suspended  at  the  desired  depth  from  an- 
other body  floating  at  or  just  beneath  the  surface,  and 
of  such  a  form  and  size  as  to  offer  less  resistance  to  the 
stream  than  the  first,  so  that  without  sensible  error  the 
velocity  with  which  the  floats  are  carried  along  by  the 
current  is  that  of  the  submerged  body  and  of  the 
stream  at  the  particular  depth  below  the  surface  at 
which  it  is  placed. 

For  the  surface-float  a  block  or  ball  of  wood  is  often 
used,  but  hollow  floats,  such  as  glass  or  metallic  balls, 
are  preferred  by  many  engineers,  as  they  may  be  par- 
tially filled  with  water  and  sunk  just  below  the  surface, 
where  they  are  less  affected  by  the  wind.  A  small  flag 
or  other  suitable  indication  will  locate  the  position  of 
the  float. 

For  the  sub-surface-floats  metallic  balls  have  been 
used  from  6  to  8  inches  in  diameter.  Humphreys  and 
Abbot,  in  their  work  on  the  Mississippi,  used  small 
kegs  without  top  or  bottom,  ballasted  with  strips  of 
lead  so  as  to  sink  and  remain  upright ;  these  kegs  were 
9  inches  high  and  6  inches  in  diameter,  but  for  depths 
greater  than  5  feet  below  the  surface  a  larger  size,  12 
inches  high  and  8  inches  in  diameter,  was  used. 

A  very  convenient  form  of  float  is  made  by  joining 
two  sheets  of  galvanized  iron  at  right  angles,  intersect- 
ing in  their  centre  lines,  and  weighting  the  lower  edges 
with  lead.  This  maintains  the  float  in  an  upright 
position  and  gives  the  required  tension  on  the  connect- 
ing cord.  The  vanes  should  be  from  8  to  20  inches 
high,  depending  upon  the  depth  of  stream  in  which 
they  are  to  be  used.  Cylindrical  air-cavities  are  pro- 
vided along  the  upper  edges  of  the  vanes. 


AND    THE  MEASUREMENT  OF  POWER.         l8l 

By  connecting  the  upper  and  lower  floats  with  a  fine 
wire,  chain,  or,  preferably,  a  braided  silk  cord,  and 
varying  its  length,  we  shall  obtain  the  several  veloci- 
ties at  varying  depths.  The  mean  of  all  these  observed 
velocities  may  be  assumed  to  be  the  average  velocity 
of  the  current. 

To  obtain  the  mean  velocity  in  a  perpendicular  by  a 
single  measurement,  a  floating  rod  is  employed.  This 
rod  may  be  either  of  wood  or  tin  in  sections  screwed 
together  for  convenience ;  the  lower  section  being 
fitted  with  a  hollow  metal  cap  which  is  filled  with 
enough  shot  or  gravel  to  cause  it  to  sink  to  the  re- 
quired depth  and  to  maintain  a  nearly  vertical  position. 
The  immersion  of  the  rod  should  be  at  least  nine 
tenths  of  the  depth  of  the  water,  which  should  not  be 
more  than  20  to  25  feet. 

If  the  channel  were  of  uniform  depth,  and  the  rod 
reached  to  the  bottom  without  actually  touching,  then 
the  velocity  of  the  rod  would  be  very  nearly  the  mean 
velocity  of  all  the  filaments  in  the  vertical  plane  through 
which  the  rod  passes.  As  the  rod  does  not  reach  the 
bottom,  its  velocity  can  only  record  the  mean  velocity 
of  the  filaments  in  a  vertical  plane  to  a  depth  equal  to 
its  immersion. 

In  general  the  rod-float  will  give  for  small  channels 
more  reliable  results  than  those  obtained  by  the  use  of 
the  double  ball-float. 

To  obtain  the  velocity  or  rate  of  motion  of  floats, 
two  parallel  range  lines  are  laid  off  on  shore,  from  100 
to  200  feet  apart,  and  the  float  placed  in  the  current  at 
some  distance  above  the  first  range-lines.  Two  tran- 
sits are  usually  employed  for  timing  the  floats,  one 


1 82  D  YNA MOME  TERS 

being  set  on  each  range.  In  addition  two  time-keepers 
will  be  required  to  take  the  exact  time  on  stop-watches 
when  signalled  by  the  observer  at  the  transit. 

If  the  stream  is  not  too  wide,  the  passage  of  the  float 
across  the  fixed  ranges  may  be  noted  by  a  single  ob- 
server using  only  a  stop-watch  and,  if  occasion  require 
it,  a  field-glass.  The  watch  is  started  when  the  float 
crosses  the  first  line,  then  the  observer  walks  to  the 
lower  station  and  stops  the  watch  the  instant  the  float 
passes  the  range-line.  The  total  distance,  s,  divided 
by  the  number  of  seconds,/,  will  give  the  mean  observed 
velocity,  v,  of  the  float,  or 

s 

v  =  -. 
t 

On  account  of  the  uncertainty  of  float-measurements, 
due  to  action  of  the  wind,  local  currents,  eddies,  and 
other  causes,  several  observations  should  be  taken  to 
obtain  a  fair  average  value  of  the  velocity. 

Approximate  determinations  of  the  mean  velocity 
of  a  stream  in  any  vertical  may  be  made  from  a  single 
measurement  by  obtaining  either  the  mid-depth  ve- 
locity or  the  surface-velocity,  and  multiplying  such 
velocity  by  a  coefficient. 

It  has  been  shown  that  the  curve  plotted  for  the 
velocity  of  the  filaments  in  a  vertical  will,  in  general, 
be  represented  by  a  parabola  whose  axis  is  parallel  to 
and  beneath  the  surface,  except  when  the  wind  is 
down-stream  with  a  rate  equal  to  or  greater  than  the 
velocity  of  the  current.  According  to  Humphreys  and 
Abbot  the  axis  of  the  parabola,  or  filament  of  maxi- 
mum velocity,  will  approach  the  surface  or  recede  from 


AND    THE  MEASUREMENT  OF  POWER.         183 

it,  depending  upon  the  direction  and  intensity  of  the 
wind.  This  is  shown  in  Fig.  75,  which  is  taken  from 
the  report  of  Humphreys  and  Abbot.* 

When  the  air  is  calm  the  axis  will  be  found  to  lie 
about  0.3  of  the  entire  depth  of  stream  beneath  the 
surface.  A  down-stream  wind  brings  the  axis  nearly 

Telocifies'in  feet  per  second. 
7.5  7.8  8.1 


The  scale  of  wind  forces  varies  from  0  (calm)  to  10  (hurricane). 
KIG.  75. — VELOCITY  OF  CURRENT  AT  VARYING  DEPTHS. 

to  the  surface,  while  with  the  wind  up-stream  it  is 
found  below  the  mean  depth.  It  will  be  noticed  that 
these  curves  intersect  at  about  mid-depth,  from  which 
it  is  inferred  that  the  velocity  of  the  mid-depth  fila- 
ment is  not  affected  by  the  wind.f 


*  Physics  and  Hydraulics  of  the  Mississippi  River. 

f  For  an  exhaustive  discussion  of  velocity  of  currents,  see  Hering 
&  Trautwine's  translation  of  Ganguillet  &  Kutter's  General  Formula 
for  Flow  of  Water  in  Rivers. 


1 84  D  YNAMOME  TERS 

This  mid-depth  velocity  will  represent  very  closely 
the  mean  velocity  of  the  vertical,  being  from  one  to 
six  per  cent  greater,  according  to  the  velocity  of 
stream,  depth,  and  roughness  of  bed.  Hence  by 
taking  the  different  station  or  division  mid-depth 
velocities  and  applying  a  coefficient  of  from  0.96  to 
0.98,  the  mean  velocity  of  the  sub-section  will  be  ob- 
tained. 

The  other  method — that  of  measurement  from  sur- 
face velocity  alone — has  been  employed  to  a  consider- 
able extent,  but  it  must  be  remembered  that  the 
results  are  only  approximate,  and  for  this  reason  should 
be  used  only  for  rough  estimates.  From  many  experi- 
ments to  determine  the  mean  velocity  in  a  vertical  from 
its  measured  surface  velocity,  it  has  been  found  that  if 
the  observation  be  taken  when  there  is  no  sensible 
wind,  the  mean  velocity  of  the  current  may  vary  from 
O.8  to  0.9  of  the  surface  velocity.  If  a  mean  value  of 
0.85  be  used  for  the  coefficient,  the  discharge  calculated 
from  the  average  of  all  the  surface  velocities  thus  ob- 
tained may  be  assumed  to  approximate  the  actual 
discharge  within  a  limit  of  from  ten  to  twenty  per 
cent.  For  obtaining  the  surface  velocity  a  current- 
meter  should  be  used. 

The  method  of  measurement  by  water-meters  is 
often  employed  to  ascertain  the  quantity  of  water  used 
by  a  motor  when  the  latter  is  supplied  through  a 
small  pipe. 

The  water-meter  consists  essentially  of  a  case, 
divided  into  two  parts,  supplied  with  plungers  or  other 
suitable  mechanism  by  which  the  volume  of  water  which 
passes  through  the  meter  in  a  given  time  (stroke  or 


AND    THE  MEASUREMENT  OF  POWER.         185 

revolution)  may  be  measured.  A  convenient  register 
is  attached,  similar  in  appearance  to  that  used  in  the 
more  familiar  gas-meter,  by  which  the  quantity  of  water 
passing  through  the  meter  may  be  read  directly  in 
cubic  feet. 

The  accuracy  of  water-meters  depends  upon  their 
construction,  and  in  all  cases  where  such  meters  are 
used  for  tests  the  readings  of  the  instrument  should 
be  carefully  compared  with  the  actual  flow  as  measured 
by  the  use  of  a  tank  of  known  capacity.  Any  error 
thus  ascertained  will  furnish  a  constant  for  correction 
when  the  meter  is  in  use. 

A  recent  form  of  water-meter  has  been  experimented 
upon  by  Mr.  Clemens  Herschel,  in  which  a  compound 
tube  provided  with  piezometers  is  used  to  determine 
the  discharge.  This  apparatus  is  constructed  upon  the 
results  of  experiments  by  Venturi  which  show  that 
when  water  flows  through  a  pipe  of  which  the  section 
is  contracted  and  subsequently  gradually  increased, 
the  pressure  in  the  smallest  section  is  much  less  than 
in  the  largest  on  either  side  of  the  contraction,  and 
may  with  suitable  proportions  sink  below  the  atmos- 
pheric pressure,  so  that  it  can  be  measured  by  a 
vacuum-gauge.  The  velocity  in  the  smallest  section  is 
theoretically  that  due  to  the  effective  head  correspond- 
ing to  the  difference  between  the  pressure  in  the 
largest  section  before  the  contraction  and  that  in  the 
smallest  section,  plus  the  influence  of  the  velocity  in 
the  largest  section,  generally  very  slight.  To  obtain 
the  actual  velocity,  the  theoretical  quantity  has  to  be 
multiplied  by  a  coefficient  to  be  determined  by  experi- 
ment. 


1 86  /)}  \VA  MOVE  TERS 

When  the  latter  is  known,  and  also  the  area  of 
section  of  the  smallest  part  of  the  pipe,  the  true 
velocity  cf  flow  can  be  determined  from  the  observed 
difference  of  pressures.* 

The  method  of  measuring  the  flow  of  water  over 
weirs  is  that  usually  employed  in  testing  the  larger 
hydraulic  motors,  for  the  reason  that  it  is  generally 
the  most  convenient  and  practicable.  The  stream 
to  be  measured  is  dammed  by  a  weir  and  all  the 
water  compelled  to  flow  through  a  rectangular  open- 
ing at  the  top.  Occasionally  the  weir  is  suppressed 
or  drowned  and  the  water  is  allowed  to  fall  over 
the  whole  length  of  the  weir,  in  Which  case  the 
sides  of  the  conduit  or  head-race  should  be  parallel  and 
vertical  for  some  distance  up-stream  above  the  weir. 

If  h  denote  the  height  in  feet  of  the  water-level 
above  the  edge  of  weir, —  measured  a  few  feet  back 
from  the  sill  before  the  sheet  of  water  begins  to  curve 
downwards, — L  the  length  of  the  weir-opening  in  feet, 
then  the  theoretical  quantity  of  water  discharged  per 
second  can  be  shown  to  be 

Q  =  \Lh  V^gh. 

The  results  of  experiments,  however,  show  that  the 
actual  quantity  is  less  than  this,  therefore  a  coeffi- 
cient must  be  used  to  determine  the  correct  amount. 

It  has  been  found  that  the  coefficient  varies  with  th« 
following  dimensions  and  conditions  : 

Length  of  weir ; 

Height  of  water  over  weir  ; 

*  Bodmer  :  Hydraulic  Motors.  See  also  "The  Venturi  Water- 
meter,"  Trans.  A.  S.  C.  E.,  Nov.  1887. 


AND    THE  MEASUREMENT  OF  POWER.         187 

Width  of  canal  of  approach  or  head-race  ; 

Nature  and  thickness  of  edges  of  weir; 

Distance  from  bottom  of  weir  to  bottom  of  conduit. 

When  the  length  of  opening  in  weir  is  less  than  the 
width  of  head-race,  so  that  the  opening  has  thin  edges 
at  the  ends,  it  is  said  to  have  end-contractions,  since 
the  thin  ends  cause  the  stream  of  water  to  contract  in 
flowing  through. 

The  formula  deduced  by  Francis*  from  experiments 
on  weirs  from  ten  to  twenty  feet  wide  and  from  seven 
to  nineteen  inches  depth  of  water  over  crest,  is 

Q  =  0.623  X  \Lh  V~2gk', 
or,  as  it  is  generally  written, 


when  there  are  no  end-contractions,  and 


when  end-contraction  occurs  and  n  (usually  2)  is  the 
number  of  end-contractions. 

To  secure  accurate  results,  the  up-stream  edge  of 
the  crest  of  the  weir  is  made  straight,  sharp,  and 
smooth  —  usually  by  constructing  it  with  an  iron  edge, 
bevelled  sharply,  and  fitting  similar  apertures  at  the 
sides.  The  depth  of  the  water  below  the  crest  of  the 
weir  should  be  not  less  than  one-third  of  the  length  of 
the  weir  ;  otherwise  the  velocity  of  approach  must  be 


*  Lowell  Hydraulic  Experiments. 


i88 


D  YNA  MOME  TERS 


considered,  as  this  tends  to  increase  the  volume  of 
water  carried  over.  Air  should  have  free  access  to  the 
space  under  the  sheet  as  it  flows  over  the  crest. 

A  more  exact  determination  may  be  obtained  by  the 
use  of  the  following  coefficient  tables  computed  by 
Mr.  Hamilton  Smith,  Jr.,*  from  the  experiments  of 
Poncelet,  Lesbros,  Francis,  Fteley  &  Stearns,  and 
others,  in  which  a  separate  coefficient  is  given  for 
varying  lengths  of  weir  and  under  different  heights 
above  crest  of  weir. 

TABLE   X. 

COEFFICIENTS  FOR  DISCHARGE  OVER  WEIRS:  Twa  END-CONTRACTIONS. 
Coefficient  =  c  in  formula  Q  -  c  X 


Effective 

L  =  Length  of  Weir  in  Feet. 

Head  in 
Feet. 

.66 

• 

2 

3 

4 

5 

7 

10 

'5 

19 

.1 

.632 

•639 

.646 

.652 

•653 

•653 

.654 

.655 

•655 

•  656 

•15 

.619 

.625 

•634 

.638 

.639  .640 

.640 

.641 

.64a 

.642 

.2 

.611 

.618 

.626 

.630 

.631   .631 

•  632 

.633 

•634 

•634 

•25 

.605 

.612 

.621 

.624 

.625-  .626 

.627 

.628 

.628 

.629 

•  3 

.601 

.608 

.6l6 

.619 

.621   .621 

.623 

.624 

.624 

.625 

•  4 

•595 

.601 

.609 

.613 

.614  .615 

.617 

.618 

.619 

.620 

•  5 

.590 

•596 

.605 

.608 

.6lO  .611 

.613 

.615 

.616 

.617 

.6 

.587 

•593 

.601 

.605 

.607:  .608 

.611 

.613 

.614 

•  7 

.585 

•590 

•598 

.604  .606 

.609 

.612 

•  613 

;6?4 

.8 

•595 

.600J  .602  .604 

.607 

.611 

.612 

.613 

•9 

•592 

.598  .600 

.603 

.606 

.609 

.611 

.612 

.0 

.590 

•595 

•598 

.601 

.604 

.608 

.610 

.611 

.1 

•587 

•593 

.596 

•599 

.603 

.606 

.609 

.610 

.2 

•585 

•  591 

•594 

•597 

.601 

.605 

.608 

.610 

•  3 

.582 

.589 

.592 

.596 

•599 

.604 

.607 

.609 

•  4 

.580 

•587 

.590 

•594 

•  598 

.602 

.606 

.609 

-5 

•  585 

•589 

•592 

•596 

.601 

.605 

.608 

.6 

.582 

.587 

.591 

•  595 

.600 

.604 

.607 

•  7 

•594 

•599 

.603 

.607 

Smith's  Hydraulics.       Wiloy  &  Sons,  1886. 


AND    THE  MEASUREMENT  OF  POWER.         189 

The  heads  in  the  first  column  are  the  effective 
heads,  and  in  such  cases  when  the  water  approaches 
the  weir  with  a  sensible  velocity  the  head  ti  due  to 


that  velocity  \k'  =  —  J    must  be    used    in   connection 

with  the  head  h  over  the  weir,  in  which  case  the  effec- 
tive head  may  be  considered  equal  to  h  -j-  1.4/1';  hence 


As  an  example  of  the  application  of  the  table, 
the  following  is  taken  from  Merriman's  "  Hydraulics." 
Let  it  be  required  to  find  the  discharge  per  second 
over  a  weir  4  feet  long  when  the  head  h  is  0.457  foot, 
there  being  no  velocity  of  approach. 

From  the  table  the  coefficient  of  discharge  is  0.614 
for  k  =  0.4,  and  0.610  for  h  =  0.5,  which  gives  about 
0.612  for  Ji  =  0.457.  Then  the  discharge  per  second  is 

Q  —  .612  X  |  X  8.02  X  4  X  V'OiTT)1  =  4-°4  CLlbic  feet 


If  the  width  of  the  feeding-canal  be  7  feet  and  its 
depth  below  the  crest  be  1.5  feet,  the  velocity-head 
will  be 

h'  =  -^  =  0.015557;'; 

but    the    velocity    v  =  quantity  of   water    discharged, 
divided  by  the  area  of  the  stream  ;  hence 

Q*  (4-04)3 


(7  X  (i-5  +  -457))" ' 


1  9O  D  YNA  MO  ME  TERS 

the  velocity-head  then  becomes 


h'  =  °-OI55s  =  o-001  34  foot. 

The  effective  head  now  becomes  h-\-  1.4/1'  =  0.459  foot, 
and  the  discharge  per  second  is 
Q  =  .612  X  1  X  8.02  X  4  X  V/(459)'  =  4-O7  cubic  feet. 

As  this  result  depends  upon  the  degree  of  accuracy 
with  which  the  quantities  used  are  ascertained,  and 
also  upon  a  possible  slight  error  in  obtaining  the  coeffi- 
cient, it  may  be  assumed  that  a  probable  error  of  at 
least  one  per  cent  exists  in  the  final  result. 

It  will  be  evident  that  as  the  velocity-head  //'  is 
small  compared  with  the  head  over  weir,  the  latter 
may  be  used  as  the  effective  head,  with  no  appreciable 
error,  in  selecting  a  coefficient  from  the  table  for  the 
first  approximation. 

The  method  of  measurement  over  weirs  is  often  em- 
ployed in  testing-flumes  by  constructing  the  tail-race 
with  a  rectangular  opening,  through  which  the  dis- 
charge which  flows  from  the  motor  is  measured  in  the 
manner  just  described. 

The  determination  of  the  height  of  water  over  weirs 
requires  considerable  care  for  accurate  tests,  on  ac- 
count of  the  small  height  generally  involved.  For 
this  purpose  some  form  of  the  Boyden  hook-gauge  is 
usually  employed. 

The   instrument,*  shown   in   Fig.  76,  consists   of   a 

*  Made  by  W.  &  L.  E.  Gurley,  Troy,  N.  Y. 


AND    THE   MEASUREMENT  OF  POWER.         19 l 

wooden  frame  3  feet  long  and  4  inches  wide,  in  a  rect- 
angular groove  of  which  another  piece  is  made  to  slide 
carrying  a  metallic  scale  divided  to  feet  and  hun- 
dredths,  and  figured  from  O  to  2^  feet,  as 
shown. 

Connected  with  the  scale  is  a  brass  screw 
passing  through  a  socket,  fastened  to  another 
shorter  sliding  piece,  shown  above,  which  can 
be  clamped  at  any  point  on  the  frame,  and 
the  scale  with  hook  moved  in  either  direction 
by  the  milled-head  nut. 

There  is  also  a  vernier  attached  to  the 
frame,  and  movable  under  the  screw-heads 
which  secure  it,  in  order  to  adjust  its  zero 
to  correspond  with  the  point  of  the  hook 
when  setting  the  gauge.  The  vernier  reads 
to  thousandths  of  a  foot. 

The  form  of  hook-gauge  designed  by  Emer- 
son and  used  in  the  Holyoke  testing-flume  is 
shown  in  Fig.  77.  In  this  gauge  a  small  gear 
operated  by  a  worm  engages  a  finely  cut  rack 
on  the  back  of  the  scale-rod  which  permits 
a  very  close  adjustment  of  the  hook,  the 
vernier  being  arranged  to  read  to  ten-thou- 
sandths of  a  foot. 

When  in  use  the  hook  is  raised  from  below 
the  level  of  the  water  until  its  point  barely 
pricks  the  surface,  when  it  will  be  noticed  that  a  slight 
swell  and  distortion  of  the  reflected  light  is  caused  just 
above  the  point  of  the  hook ;  by  carefully  lowering 
the  hook  until  this  distortion  disappears,  the  point 
may  be  assumed  to  be  at  the  level  of  the  water,  which 


192 


DYNAMOMETERS 


can  then  be  read  from  the  vernier. 
The  instrument  is  supposed  to  have 
been  previously  set  with  its  vernier  at 
zero,  when  the  point  of  the  hook  was 
exactly  on  a  level  with  the  sill  of  the 
weir. 

The  hook-gauge  is  generally  enclosed 
in  a  wooden  case  or  box  open  at  the 
top,  and  provided  with  a  small  inlet  at 
the  bottom,  in  order  to  prevent  any  dis- 
turbance of  the  water  in  the  vicinity  of 
the  hook.  As  previously  stated,  the 
measurement  of  the  head  over  the 
weir  must  be  taken  several  feet  back  of 
the  crest,  where  the  water  is  level. 

To  allow  the  observations  to  be  taken 
more  readily,  the  water  may  be  led  by 
a  hose  or  other  pipe  from  the  bottom 
of  the  race-way  above  the  weir  (up- 
stream) into  the  hook-gauge  box,  which 
may  be  placed  at  any  convenient  point 
near  by. 

Very  accurate  results  may  be  obtained 
by  the  use  of  a  good  levelling-rod  with  a 
hook  secured  to  the  foot ;  the  slide  may 
be  operated  by  a  small  gear  and  rack 
which  can  be  attached  to  the  rod  to 
allow  a  fine  adjustment  of  the  hook. 

The  total  head  or  fall  can  be  obtained 
very  precisely  by  the  use  of  a  hook,  at 
the  level  of  the  water  in  the  tail-race, 
secured  to  a  graduated  rod  placed  beside 


FIG.  77. 


AND    THE   MEASUREMENT  OF  POWER.         193 

a  fixed  cylinder  with  glass  tube  attached,  which  is  con- 
nected by  means  of  a  rubber  hose  with  the  upper  water- 
level.  By  this  arrangement  the  reading  on  the  scale 
at  the  water-level  in  the  glass  tube  will  give  the  total 
height  between  the  two  levels — the  graduations  on  the 
rod  being  a  measure  of  the  distance  from  the  point  of 
the  hook.* 

Another  method  of  obtaining  the  total  head  is  to 
run  a  line  of  levels  from  one  to  the  other.  Permanent 
bench-marks  being  established,  gauges  can  then  be  set 
in  the  head  and  tail  races,  and  graduated  so  that  their 
zero-points  will  be  at  some  datum  below  the  tail-race 
level.  The  difference  in  readings  will  give  the  required 
total  head.f 

Simpler  methods  will  suggest  themselves  and  may 
be  used  where  less  accuracy  is  required,  as  in  rough 
estimates  of  water-power. 

As  water  in  most  cases  where  available  for  power 
has  a  commercial  value,  the  most  advantageous  and 
profitable  use  of  it  should  be  considered. 

In  this  relation  not  only  the  efficiency  of  the  motor 
employed,  but  the  pipes  which  supply  the  motive 
power  have  an  important  bearing  upon  the  result. 

When  water  is  delivered  to  a  hydraulic  motor 
through  a  pipe  or  nozzle,  as  in  the  numerous  class  of 
small  motors  fed  from  a  city  main,  the  diameter  and 
length  of  pipe,  as  well  as  the  size  and  shape  of  nozzle, 
largely  affects  the  work  done  on  the  motor. 

The   head    is   not   that    due  to  difference  in  levels 

*  R.  H.  Thurston.     Trans.  A.  S.  M.  E.,  vol.  vui. 
f  Merriman's  Hydraulics,  p.  288. 


1  94  D  YNA  MOME  TERS 

between  the  reservoir  and  the  motor,  but  is  much  less 
on  account  of  losses  in  transmission  due  to  friction  in 
the  pipes,  loss  at  entrance,  loss  due  to  bends  and  angles 
in  the  pipe,  changes  in  cross-section,  and  other  causes. 

As  any  loss  of  head  is  a  direct  loss  of  power,  such 
loss  should  be  prevented  as  much  as  the  circumstances 
in  the  case  will  justify.  Where  both  the  water-supply 
and  head  are  limited,  such  pipe  should  be  put  down  as 
will  avoid,  as  far  as  possible,  serious  loss  in  the  head  or 
supply  ;  where,  on  the  other  hand,  water  is  abundant 
and  a  very  considerable  head  can  be  obtained,  a  loss 
in  this  way  may  be  justified  to  a  larger  extent  to  save 
cost  of  pipe. 

The  greatest  loss  in  long  pipes  is  that  due  to  friction, 
which  loss  may  be  deduced  approximately  from  the 
following  formula  : 


in  which  hl  =  height  of  resistance  of  friction,*  /a  co- 
efficient obtained  by  experiment  for  different  condi- 
tions, /  the  length  of  pipe  in  feet,  d  its  diameter  in 
feet,  and  v  the  velocity  of  water  in  feet  per  second. 
The  coefficient  of  friction,/,  is  not  constant,  but  varies 
with  the  velocity  and  with  the  diameter  and  internal 
condition  of  the  pipe. 

From  this  it  will  be  seen  that  the  loss  due  to  friction 
is  independent  of  the  pressure  of  the  water  ;  that  it  is 
proportional  to  the  length  of  pipe  ;  that  it  increases 
nearly  with  the  square  of  the  velocity  ;  that  it  is  in- 

*  Weisbach. 


AND    THE   MEASUREMENT  OF  POWER. 


195 


versely  proportional  to  diameter  of  pipe ;  and  that  it 
decreases  with  the  smoothness  of  the  pipes  and  joints. 

The  coefficient,  f,  varies,  according  to  Merriman, 
from  o.oi  to  0.05  and  is  often  assumed  in  approximate 
calculations  at  0.02. 

The  following  table  of  coefficients  for  smooth  clean 
iron  pipes  obtained  from  deductions  of  Fanning,  Smith, 
and  others  has  been  compiled  by  Prof.  Merriman, 
and  will  give  the  value  to  use  in  any  particular  case, 
from  which  the  probable  loss  due  to  friction  may  be 
obtained. 


TABLE  XI. 
FRICTION  FACTORS  FOR_SMOOTH,  CLEAN  IRON  PIPES. 

Coefficient  = /in  formula  hi  =/—  — . 
d  zg 


D    meter 
i     Feet. 

Velocity  in  Feet  per  Second. 

• 

• 

3 

4 

6 

10 

IS 

•05 

0.047 

0.041 

0.037 

0.034 

0.031 

O.O29 

O.O28 

.038 

.032 

.O3O 

.02& 

.026 

.024 

.023 

•25 

.032 

.028 

.026 

•  025 

.024 

.022 

.O2I 

.5 

.028 

.026 

.025 

.023 

.022 

.O2O 

.Oig 

•75 

.026 

.025 

.024 

.022 

.021 

.Oig 

.018 

•  025 

.024 

.023 

.022 

.020 

.018 

.017 

•25 

.024 

.023 

.022 

.O2I 

.Oig 

.017 

.Ol6 

•  5 

-023 

.022 

.O2I 

.O2O. 

.Ol8 

.016 

•  015 

•75 

.022 

.021 

.020 

.018 

.017 

•  015 

.014 

2. 

.021 

.O2O 

.Oig 

.017 

.Ol6 

.014 

.013 

2-5 

.020 

.Oig 

.018 

.Ol6 

•015 

-013 

.012 

3- 

.Oig 

.018 

.016 

.015 

.014 

•013 

.012 

3-5 

.Ol8 

.017 

.Ol6 

.014 

.013 

.012 

4- 

.017 

.Ol6 

.015 

•  013 

.012 

.Oil 

.016     ' 

•  015 

.OI4 

.013 

.OI2 

6'. 

.015 

.014 

.013 

.012 

.Oil 

1  96  D  YNA  MOME  TERS 

The  loss  of  head  due  to  resistance  as  the  water  en- 
ters a  pipe  will  vary  with  the  form  of  mouthpiece  em- 
ployed, and  may  be  taken  as 


for  average  cases,  although  with  a  perfect  bell-shaped 
mouthpiece  this  loss  will  be  zero. 

For  long  pipes  the  loss  due  to  entrance  is  very  slight, 
as  compared  with  the  loss  due  to  friction. 

The  other  losses  which  occur,  such  as  those  due  to 
change  of  cross-section,  angular  connections,  curvature 
of  bends,  and  resistance  of  valves,  are  not  so  readily 
obtainable. 

Where  the  radius  of  curvature  is  great  as  compared 
to  the  diameter  of  pipe,  and  few  bends  occur  in  the 
pipe,  the  loss  will  be  small  ;  also  where  conical  reduc- 
ers are  used  when  changing  from  one  diameter  to 
another,  the  loss  for  each  change  will  be  barely  ap- 
preciable and  may  be  neglected. 

Moreover,  as  the  actual  conditions  are  generally 
unknown,  these  latter  losses  will  have  to  be  neglected 
in  ordinary  computations,  and  the  formula  for  the 
velocity  will  then  be  that  obtained  for  pipes  compara- 
tively straight,  smooth,  and  of  essentially  the  same 
diameter. 

Assuming  the  general  formula 

*=£. 

2g 

we  can  obtain  the  velocity  of  flow  corresponding  to  a 
given  hydrostatic  head  from  V  '=  VUgh'  if  no  losses 


AND    THE  MEASUREMENT  OF  POWER.         1$? 

occur  in  the  pipe  ;  but  if  the  velocity-head  of  the  issu- 

ed 

ing  stream  equal  —  •  the  losses  in  the  pipe  will  then  be 

equal  to  the  hydrostatic  head  minus  the  velocity-head, 

v* 
hence  equal  to  //'  --  — 

This  loss  must  be  equal  to  the  sum  of  the  losses  due 
to  friction,  and  to  entrance  (provided  the  lesser  resist- 
ances due  to  curvature  and  other  causes  be  neglected)  ; 
therefore 


By  substituting  the  values  previously  found  for  h^  and 
//,  there  is  obtained 


or 


which  is  a  convenient  formula  to  use  in  obtaining  the 
velocity  of  flow  in  straight  pipes  of  uniform  diameter, 
from  which  the  head  corresponding  to  this  velocity  may 
be  obtained  by  substitution  in  the  general  formula 

V» 
h  =  —  •     The  head,  h! ',  necessary  to  overcome  the  re- 


D  YNA  MOME  TERS 


sistances  in  a  given  length  and  diameter  of  pipe  and  to 
maintain  the  velocity,  v,  may  be  calculated  from 


If  a  given  supply  of  water,  Q,  be  required  per  second, 
the  theoretical  area  of  pipe  will  be  A  =  \nd* ;  therefore 


the  velocity  in  the  pipe  will  be  v  =  ^  =  — r2 ;  hence 

/i         Ttu 

the  theoretical  head  required  to  maintain  the  flow  will  be 

osr  *(«*+/$ 


provided  the  inner  surface  of  the  pipe  be  reasonably 
smooth.  If  an  iron  pipe  be  unprotected  by  any  surface 
coating  it  will  in  time  become  coated  with  scale  or  lime 
deposits  and  more  or  less  tuberculated.  These  depos- 
its affect  the  discharge  in  a  twofold  manner :  first  by 
reducing  the  area  of  pipe,  and  secondly  by  increasing 
the  roughness.  Therefore  to  reduce  the  loss  as  much  as 
possible  it  will  be  an  advantage  to  cover  the  inner  sur- 
face with  coal-tar  varnish  or  some  other  suitable  coat- 
ing. 
In  any  case  the  velocity-head  of  the  issuing  jet  will  equal 

v1 

— ;  hence  if  the  discharge,  Q,  and  also  the  area,  a,  of  jet 

<£» 

be  known,  the  velocity,  v,  can   be   determined    from 

*  For  a  discussion  of  the  loss  due  to  bends,  curvature,  reduction  in 
area,  resistances  in  valves  and  cocks,  see  Weisbach,  Coxe's  transla- 
tion, pages  874  et  seq. 


AND    THE  MEASUREMENT  OF  POWER.         199 

Q  V*          Q* 

v  =  —-,  therefore  —  =  -  5,  and  the  velocity-head  will 

then  be 

h          Q* 

0  -  W 

In  the  determination  of  the  value  of  the  area,  a,  of 
issuing  stream  the  general  method  employed  is  to 
caliper  the  jet  at  its  least  cross-section.  By  carefully 
ascertaining  the  diameter  of  jet  for  a  given  orifice  or 
tube  and  comparing  the  area  of  latter  with  the  area  of 
jet  there  is  obtained  a  value,  C',  which  may  be  used  as 
a  coefficient  in  obtaining  actual  contraction  for  a  given 
opening. 

Thus  if  a  equals  the  area  of  jet,  and'  A  equals  area 
of  circular  orifice  in  a  thin  plate,  there  is  obtained 


_ 

~  A  ~ 

where  d  =  diameter  of  jet  and  D  —  diameter  of  orifice. 
The  average  value  of  C'  thus  found  =  0.62. 

If  the  orifice  have  rounded  or  curved  edges,  the  con- 
traction will  be  very  much  diminished  and  the  coeffi- 
cient will  be  found  to  vary  from  0.62  to  i.o. 

If  the  actual  quantity  of  wrater  which  flows  through 
an  orifice  in  a  given  time  be  measured,  there  will  be 
found,  as  in  the  case  of  flow  over  weirs,  that  this  quan- 
tity is  much  less  than  the  theoretical  discharge  calcu- 
lated for  the  area  of  opening  under  the  given  head  ; 
therefore  the  theoretical  discharge  must  be  multiplied 
by  a  coefficient  C  in  order  to  determine  the  actual  dis- 
charge. 


20O  D  YNA  MOME  TERS 

This  coefficient  of  discharge  varies  from  about  0.59 
to  0.64  for  circular  orifices  in  a  thin  plate,  depending 
upon  the  size  of  orifice  and  the  head.  For  ordinary 
cases  the  coefficient  of  discharge,  C,  =  0.61  may  be  as- 
sumed. 

It  can  be  shown  further  that  the  velocity  of  flow 
through  an  orifice  in  a  thin  plate  is  diminished  about 
two  per  cent  by  friction,  and  that  the  theoretical  veloc- 
ity must  be  multiplied  by  a  coefficient  to  obtain  the 
actual  velocity.  This  coefficient  of  velocity  Ct  will 
vary  slightly,  increasing  with  the  head,  but  0.98  may 
be  assumed  to  meet  most  conditions. 

It  will  be  noticed  that  the  coefficient  of  velocity  is 
equal  to  the  ratio 

coefficient  of  discharge    _  C  _ 


coefficient  of  contraction       C1 

From  these  considerations  it  will  be  seen  that  the 
circular  orifice  in  a  thin  plate  offers  another  method  of 
ascertaining  the  discharge.  If  the  area  of  reservoir  or 
supply-tank  be  large  compared  to  area  of  orifice,  and 
if  the  head,  /*,  at  centre  of  orifice  in  a  vertical  plane  is 
large  compared  with  the  diameter  of  opening,  the  theo- 
retical discharge  may  be  assumed  equal  to 


therefore  the  actual  discharge  will  be  CQ!  —  Q,  hence 
0.61  nd*    .  —  - 


AND    THE  MEASUREMENT  OF  POWER.        2OI 

As  it  is  impracticable  to  place  the  buckets  or  vanes  of 
a  water-motor  sufficiently  near  an  orifice  to  utilize  the 
energy  of  the  jet,  short  tubes,  nozzles,  or  tips  are  used 
for  this  purpose,  and  for  these  separate  coefficients  will 
have  to  be  determined. 

When  the  discharge  takes  place  through  a  short 
cylindrical  tube  whose  length  is  about  three  times  its 
diameter,  it  will  be  found  that  under  ordinary  condi- 
tions there  is  no  contraction  of  the  jet,  but  the  velocity 
of  the  stream  is  diminished  about  18  per  cent;  hence 
the  coefficient  of  velocity  C,  may  be  assumed  to  be 
0.82  for  such  short  pipe  when  the  inner  corners  are 
not  rounded.  When  there  is  no  contraction,  that  is 
when  C  —  I,  the  coefficient  of  discharge  C  will  equal 

£7 
the  coefficient  of  velocity,  since  -~-,  =  C^ ;  hence  the 

coefficient  of  discharge  in  this  case  will  equal  0.82.  It 
has  been  found  that  if  a  conical  converging  tube  be 
used,  the  coefficient  of  velocity  and  of  discharge  are 
both  very  much  higher  than  for  a  straight  tube,  and 
for  this  reason  such  tubes  or  mouthpieces  are  used, 
with  certain  modifications,  when  it  is  desired  to  utilize 
the  energy  of  flow  to  the  best  advantage.  From  ex- 
periments by  D'Aubuisson  and  Castel  *  on  conical 
tubes  with  varying  angles  of  convergence  and  with 
square  corners  at  entrance,  the  coefficient  of  discharge 
attained  its  maximum  value  of  0.946  for  a  tube  whose 
sides  converge  at  an  angle  of  13^°  ;  but  the  coefficient 
of  velocity  increased  continually  as  the  angle  increased  ; 
for  a  tube  whose  angle  was  48°  50'  the  coefficient  of 
velocity  was  0.984.  In  these  experiments  the  tube 
*  Weisbach. 


202  DYNAMOMETERS 

was  £  inch  diameter  at  small  end,  and  its  length  2.6 
times  its  diameter. 

The  results  of  Castel's  experiments  also  show  that 
under  varied  heads  the  coefficients  of  discharge  and  of 
velocity  were  practically  constant  for  the  same  mouth- 
piece. 

Some  experiments  by  Lespinasse  on  the  canal  of 
Languedoc  *  show  the  great  advantage  in  using 
converging  mouthpieces  to  effect  an  increase  in  the 
discharge  ;  the  mouthpieces  employed  were  truncated 
rectangular  pyramids  9.59  feet  long,  the  dimensions  at 
one  end  2.4  by  3.2  feet,  at  the  other  .44  by  .62  foot  ; 
their  opposite  faces  were  inclined  at  angles  of  11°  38' 
and  15°  18',  and  the  head  employed  was  9.59  feet.  The 
experiments  resulted  in  determining  a  coefficient  of 
discharge  varying  from  0.976  to  0.987. 

If  the  motor  to  be  tested  be  supplied  with  several 
conical  or  curved  mouth-pieces,  it  is  advisable  to  cali- 
brate each  one  in  order  to  obtain  its  coefficient  of 
discharge,  C. 

By  inserting  a  gauge  near  the  discharge,  in  the  sup- 
ply-pipe, which  should  be  large  relatively  to  the  nozzle, 
the  hydrostatic  head  may  be  obtained,  by  multiplying 
the  gauge-pressure  by  2.304  as  shown  hereafter.  By 
this  means  the  actual  discharge  may  be  obtained  by 
noting  the  pressure  and  calculating  the  theoretical 
discharge  for  the  given  mouth-piece  from 


then  Q'XC  will  equal  the  actual  discharge. 
*  Jackon's  Hydraulic  Manual. 


AND    THE  MEASUREMENT  OF  POWER.         2OJ 

If  we  assume  the  weight  of  a  cubic  foot  of  water  to 
be  62.5  pounds,  and  the  height  of  a  column  of  water  to 
be  h  feet,  the  total  pressure,  P,  per  square  foot  will  be 

P  =62.5/1, 
and 

h  —  .oi6P. 

As   the   pressure   is   ordinarily  given  in  pounds   per 
square  inch,  the  above  will  become 


and 

/*  =  2.3O4/. 

This  will  give  the  available  hydrostatic  head  corre- 
sponding to  a  given  pressure,  p,  in  the  pipe  as  ascer- 
tained by  the  reading  of  a  pressure-gauge  inserted  near 
the  nozzle  (see  Fig.  70,  page  168),  the  reading  of  the 
gauge  to  be  taken  when  the  water  in  the  pipe  has  no 
velocity. 

In  obtaining  the  pressure  from  a  gauge  in  order  to 
determine  the  effective  head  available  at  the  motor, 
the  pipe  to  which  the  gauge  is  connected  should  be 
inserted  in  the  supply-pipe  near  the  entrance  to  the 
nozzle,  at  right  angles  to  the  axis  of  the  supply-pipe, 
and,  preferably,  the  latter  should  be  tapped  on  one 
side  rather  than  on  top.  If  the  gauge-tube  be  inclined 
toward  the  stream  in  the  pipe  when  the  water  is  flow- 
ing through,  the  tendency  will  be  to  increase  the  press- 
ure-head; and  if  it  be  inclined  in  the  opposite  direction, 
the  reverse  will  be  the  case. 

If  the  reading  of  gauge  be  taken  when  the  motor  is 
running,  there  will  be  a  certain  diminution  of  head,  as 


204  &  YNA  MOME  TERS 

indicated  by  the  gauge,  due  to  the  velocity  of  the 
water  in  the  pipe.  When  the  diameter  of  supply-pipe 
is  large  compared  to  that  of  the  nozzle  at  discharge — 
which  is  usually  the  case,  as  the  velocity  and  energy  of 
the  water  is  best  utilized  by  such  arrangement — the 
reduction  of  pressure-head  is  barely  appreciable  and 
may  be  neglected,  as  the  error  from  this  cause  is  well 
within  the  limits  of  the  degree  of  accuracy  attained  in 
determining  other  quantities  involved. 

When,  however,  the  supply-pipe  and  nozzle  do  not 
greatly  differ  in  size,  the  velocity  in  the  pipe  approaches 
more  nearly  to  the  velocity  at  the  nozzle,  .and  the 
pressure-head  may  in  such  cases  differ  materially  from 
the  effective  head. 

If  h  equals  the  known  pressure-head,  and  ht  equals 
the  head  due  to  the  velocity,  V,  in  the  pipe,  then  the 
effective  head  will  be 

F* 
h'  =  h  +  —  ; 

2* 
the  velocity  v  at  the  end  of  the  nozzle  will  then  be 


but  since  the  same  quantity  of  water  which  discharges 
from  the  nozzle  must  pass  through  the  pipe,  the 
respective  velocities  will  be  inversely  proportional  to 
the  sectional  areas,  and  hence  to  the  squares  of  their 
respective  diameters  ;  that  is, 

v  _A  _  D^ 
V~  a~  d*' 


AND    THE  MEASUREMENT  OF  POWER.         20$ 

or 


in  which  V,  A,  and  D  represent  the  velocity  of  flow, 
area  of  cross-section,  and  diameter  of  pipe  ;  and  v,  a, 
and  d  are  the  corresponding  values  at  the  outlet  of 
nozzle. 

Substituting  this  value  of   V  \r\  the  expression  for  v, 
above,  there  is  obtained 


from  which  the  effective  head,  //'(==  — ),rnay  be  calcu- 

V       2gl 

lated.  When  the  diameter  of  pipe  is  large  compared 
to  the  diameter  of  nozzle  at  discharge,  the  ratio  —  will 
be  very  small,  in  which  case  v  =  C^  V2gh  will  approach 
v=Cl  \l2gh' ;  if  the  ratio  of  sectional  areas,  or  —  is  less 

than  one  to  ten,  the  error  in  using  //  for  h'  will  be  less 
than  one-half  of  one  per  cent,  and  when  the  ratio  is 
less  than  one  to  twenty,  h  may  be  assumed  to  equal  h' 
within  a  limit  of  .025  of  one  per  cent, — a  greater 


200  D  YNA  MOME  TERS 

degree  of  accuracy  than  can  be  obtained  from  the 
other  factors  involved. 

As  an  example,  a  motor  is  supplied  by  a  pipe  two 
inches  in  diameter  having  a  nozzle  whose  diameter  at 
discharge  equals  half  an  inch,  the  gauge-pressure  in  the 
pipe  near  the  entrance  to  the  motor  equals  43  pounds, 
and  the  coefficient  of  velocity  =  0.98. 

According  to  the  exact  formula, 


Q-96  X 


=  4/64.4  X  95-49  =  78.41  feet  per  second. 
From  the  approximate  formula 
^  =  C, 


we  find,  by  assuming  the  effective  head,  h',  equal  to  the 
pressure-head,  //, 

vt  =  .98  1/64.4  X  99.07  =  1/64.4  X  95.1  f=  78.26; 
that  is,  the  gain  in  using  the  exact  formula  will  only  be 

v        78.41 

-  =  '•— -*--  =  1.0019, 

vl       78.26 

or  about  two  tenths  of  one  per  cent,  which  can  readily 
be  neglected  without  sensibly  affecting  the  result. 


INDEX. 


Absorption-dynamometer,  Richards',  54 

"  Alden's,  56 

"  "  Fronde's,  63 

Adjustment  of  cradle-dynamometer,  103 
Air-resistance,  measurement  of,  no 
Alden's  absorption-dynamometer,  56 
Allowable  strain  in  belting,  14 
Amos  &  Appold's  brake,  33 
Approximations  for  driving  power,  3,  n 
Arc  of  contact,  influence  of,  12,  16,  17 
Area  of  channel,  measurement  of,  172 

B 

Babcock,  G.  H.,  rule  for  estimating  horse-power,  3 
Band-brakes,  28,  40 
Barrus,  friction  of  shafting,  8 
Belt  brake,  28 

"    transmission-dynamometer,  Briggs,  So 
«  "  "  Hopkinson,  79 

«'  "  "  other  forms,  94,  q6 

"    velocity  of,  used  to  determine  horse-power,  10 
Belting,  coefficient  of  friction,  15 

strength  of,  14 
Belts,  double,  17 

"       in  actual  use,  Table  of,  15      .   . 
"       slip  in,  16 

207 


2O8  INDEX. 

Belts,  specific  duty  of,  13 
"       wider,  should  be  used,  10 

Bench-marks,  173,  193 

Boyden  hook-gauge,  190 

Bracket!  cradle-dynamometer.  q8 

Brake-blocks,  48 

Brake-tests  on  engines,  27 

Brakes,  band,  31,  40 
belt,  28 
rope,  37 
"         water,  56,  63 

Buff  &  Berger's  current-meter,  175 


Calibration  of  current-meters,  178 

"  Emerson  power-scale,  116 
"  Tatham  dynamometer,  03 
Capacity  of  friction-brakes,  51 
Centrifugal  force,  effect  of,  in  power-scale,  u6 
Coefficient  of  contraction,  200 
"  discharge,  199 
"  friction  for  belting,  15 

"   flow  in  pipes,  195 
"  "  velocity,  200 

Coefficients  for  discharge  over  weirs,  188 
Compensating  brakes,  133 
Compound  scale-plate,  129 
Cradle-dynamometer,  98 
Current-meters,  171 

"         Buff  &  Berger's,  175 

calibration  of,  178 
"         Price's,  177 
"         Woltmann's  Mill,  174 


Dash-pots,  22,  47,  48,  54 
Determination  of  brake-power,  24 

"  mechanical  equivalent  of  heat,  93 


INDEX.  209 


Differential  scale-plate,  127 
Discharge  through  orifices,  199 
Dimensions  for  Prony  brake,  22 
Double  belts,  17 

Driving  power  from  velocity  of  belt,  10 
Dynamometer,  Alden,  56 

Balance,  77 

"  Belt,  94,  96 

"  Brackett,  98 

"  Briggs,  So 

Cradle,  98 

"  Differential,  76 

"  Emerson,  113 

"  Flather,  137 

"  Floating,  103 

"  Froude,  63 

"  Hartig,  in 

"  Hopkinson,  70 

"  Hydraulic,  137 

"  Marine,  63 

"  Morin,  72 

"  Reynolds,  70 

"  Richards,  54 

"  Tatham,  82,  87 

Van  Winkle    117 

"  Webb,  103 

Webber,  77 
Dynamos,  friction  in,  no 


Effect  of  increasing  load  on  water-wheel,  171 

Efficiency  of  water-wheels,  16 

Electric  register  for  current-meters,  175,  178 

Emerson  power-scale,  113 

Estimated  power,  variance  of,  14 

Experiments  on  lathes,  158,  161 

"  "  water-wheels,  167,  170 

'  with  leather  belting,  14 


2 IO  INDEX. 


Flather  hydraulic  dynamometer,  137 
Float  measurements,  173,  179 
Floating  dynamometer,  103 
Flow  of  water  over  weirs,  186 
Formula  for  brake-power,  25,  29 

"          "   measurement  over  weirs,  187 

"          "   power  required  to  drive  lathes,  \yi 
"   width  of  belt,  n,  16 

"          "    width  of  rubbing  surface,  153 
Friction  and  air-resistance,  no 
Friction,  coefficient  of,  in  belting,  15 

"         factors  for  iron  pipes,  195 

"         in  lathes,  149,  151 

"          of  shafting  in  machine-shops,  9 
"    mills,  8 

"    •      "  toothed  gears,  measurement  ol,  100 

"          "  water  in  pipes,  194 

"         work  of,  in  Prony  brake,  25 
Friction-brake,  Alden's,  56 

"       capacity  of,  51 

"  "       for  vertical  shaft,  46 

"  "        Prony,  19,  21 

"       used  to  test  locomotive,  Ol 
Froude's  absorption-dynamometer,  63 


Gas-engine  test,  38 


II 


Hartig's  experiments  on  lathes,  158 

"        transmission-dynamometer,  in 
Heinrich's  proportions  for  small  brakes,  21 
Henthorn,  J.  T.,  friction  of  shafting,  8 
Herschel,  C.,  Venturi  water-meter,  185 
Hobart,  J.  A.,  experiments  on  lathes,  161 


INDEX.  211 


Hollow  brake-strap,  50 

Hook-gauge,  190 

Hopkinson  belt-dynamometer,  79 

Horse-power  determined  from  velocity  of  belt,  n,  18 

"         "       required  to  drive  machinery,  5 
"         "      "      shafting,  5 

"         "       transmitted  by  belts  in  use,  15 
Hydraulic  dynamometer,  137 
Hydrostatic  head,  203 

I 

Improved  Alden  brake,  60 
Indicator-cards  from  dynamometer,  148 
Indicator,  use  of,  with  dynamometer,  136 

J 
Jamieson,  rope  brake,  39 

"         gas-engine  test,  38 


Kapp's  compensating  brake,  32 

L 

Lathes,  Hartig's  experiments  on,  158 
"      power  required  to  drive,  148,  151 
"       table  of  horse-power,  155 
Leads  for  sounding,  172 
Locomotive,  brakes  for,  61 

"  method  of  mounting,  61 

Loss  of  head  in  pipes,  194 
Lubrication  of  Alden  brake,  60 
"  "  brakes,  27,  48 

M 

Machinery,  power  required  to  drive,  3,  5 
Machines,  belting  of,  2 
Machine  tools,  power  required  to  drive,  136 
Marine-engine  dynamometer,  63 


212  INDEX. 

Materials  for  brake-blocks,  49 

Mean  velocity,  181,  184 

Measurement  of  friction  in  toothed  gears,  109 
"  power  from  belt  used,  10 
"  rented  power,  advantage  of,  13 
"  velocity  by  surface-floats,  179 
"  water  over  weirs,  186 
"  water-power,  165 

Metal,  power  required  to  remove,  159 

Meters,  current,  171 
"       power,  117 
water,  184 

Method  of  mounting  locomotive,  161 

Mid-depth  velocity,  182 

Moderators,  22,  47,  48 

Morin  transmission-dynamometer,  72 


Nagle,  table  of  belting,  15 

Number  of  men  employed  per  horse-power,  3,  5 


Power,  rented,  measurement  of,  13 

required  to  drive  machinery,  5 

"      "     machine  tools,  136 

"     shafting,  5 
"        "  remove  metal,  159 
"  scale,  Emerson,  113 
Power-meter,  Van  Winkle,  117 
Pressure  due  to  head,  203 
Price,  current-meter,  177 
Prony  friction-brake,  19,  21 

R 

Rappard  band-brake,  40 
Rating  current-meter,  178 
Registering  belt  dynamometer,  97 
Regulators,  22,  47,  48 


INDEX.  213 

Resistance  of  air  in  dynamos,  no 
Reynolds'  water-brake,  70 
Richards'  absorption-dynamometer,  54 
Rod  floats,  181 

Rope  brakes,  37  . 

Royal  Agricultural  Society's  brake,  33 
Rubbing  surface,  48 

Rule  for  estimating  horse-power  from  belt  used,  II 
"     "  "  "         "      from  men  employed,  3 


Shaft-dynamometer,  113,  117 

Shafting,  friction  of,  8,  9 

Shafting,  power  required  to  drive  (Table),  5 

Sibley  College  brake,  23 

Slip  in  belt,  16 

Sounding-poles,  173 

Specific  duty  of  a  belt,  13 

Spring  dynamometers,  72,  117,  131 

Strength  of  belting,  14 

Surface-velocity,  measurement  of,  179 

"  "        of  pulley  with  rope  brake,  40 


Table  of  capacity  of  friction-brakes,  51 

"      "  coefficients  for  discharge  over  weirs,  188 

"      "  dimensions  for  Prony  brake,  22 

"      "  friction  factors  for  iron  pipe,  195 

"      "  horse-power  required  to  drive  machinery,  5 

"      "      "          "  "        "      "     small  lathes,  155 

"      "      "          "  "        "  remove  metal,  161,  162 

"      "  test  of  hydraulic  motor,  170 

"      "  widths  and  velocities  of  belting,  15 

"     showing  effect  of  increased  load  on  water-wheels,  171 

Tatham's  transmission-dynamometers,  82,  87 

Tension  in  belts,  12,  18,  81 

Test  of  small  water-wheel,  167,  170 

Tests  on  engines,  27,  38 


2H  INDEX. 

Towne,  H.  R.,  experiments  on  belting,  14 

Transmission-dynamometers,  72 

Balance,  77 
Belt,  94,  96 
Briggs,  80 
Brackett,  98 
Cradle,  98 
Differential,  76 
Emerson,  113 
"  "  Flather,  139,  142 

Floating,  103 
"  Hartig,  in 

Hopkinson,  79 
Hydraulic,  137 
Morin,  72 

"  "  Tatham,  82,  87 

Van  Winkle,  137 
Webb,  103 
Webber,  77 

Turbine  brake,  63,  70 


Van  Winkle  power-meter,  117 

Velocity-head,  198 

Velocity  of  belt,  power  measured  by,  10 

"         "  belting,  15 

"         "  current  at  a  varying  depth,  183 
Vertical  friction-brake,  46 

W 
Water-brake,  60,  63,  70 

"     cooled  brakes,  23,  33,  50 

"     gauge,  173 

"      meters,  184 

"      power,  measurement  of,  165 

"     wheels,  efficiency  of,  166 

"        measurement  of,  165 
"          "        test  of,  167,  170 


INDEX,  21 S 


Webb  floating  dynamometer,  103 
Webber  balance-dynamometer,  77 
Webber,  S.,  friction  of  shafting,  8 

"         "    large  friction-brake,  47 
Weirs,  measurement  of  water  over,  186 
Westinghouse,  engine-tests,  27 

friction-brakes,  26 
Width  of  rubbing  surface,  50 
Widths  of  belt  in  actual  use,  15 
Woltmann's  Mill,  174 
Work  absorbed  by  friction,  26 
"     done  on  brake,  25,  29 


UNIVERSITY  OF  CALIFORNIA,  LOS  ANGELES 

THE  UNIVERSITY  LIBRARY 
This  book  is  DUE  on  the  last  date  stamped  below 

OCT  2  9  1954 


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